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It's probably been done but I'll try and be concise so this is a decent first post for people to follow the layout to.

Action: Black Lagoon: Probably the best balls out action anime out there...at least in my opinion as alot of the characters are very likable. Even some of the bad guys are sympathisable with throughout.
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Romance: Toradora!: The best love story ever told in my opinion. A far stronger supporting cast than most romances or in fact any genre. Each character is well developed and very relatable.
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Harem: Seto no Hanayome: Got alot of contenders in this category but this one was so funny and had such a good cast of characters that I think it edges into first for this type.
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Drama: Kanon 2006: I simply prefer it to Clannad, better characters and a better story in my opinion. This is followed closely by the Ef series though.
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Shounen: Soul Eater: I dont like the genre but this is one I could enjoy as alot of the characters had different personalities instead of the generic ones from things such as Naruto and Bleach.
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Mystery: Higurashi no Naku Koro Ni / Kai: Combination of both seasons as the mystery isnt complete without both. The first season had me guessing all the way and the second answered all my questions wonderfully.
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Slice of Life: Usagi Drop: I havent finished this, but I swear Rin is so close to my own daughter, they are even close in age. It's like watching a mirror of my own life and it can't help but make me smile.
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Seinen: Puella Magi Madoka Magica: I'd argue this is Seinen, anyone who has watched beyond episode 3 will know what I mean. A really dark anime despite how it appears.
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Horror: Another: I was going to pick Higurashi but I felt it more of a Mystery, especially in Season 2 so Another wins out in this category. Felt almost like The Ring at points and some of the deaths are quite gruesome.
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Sports: Cross Game: I was interested in Baseball for a time after watching this. I like watching a good Sports anime with a strong cast and this one delivered...at least in my eyes.
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Ecchi: Kodomo no Jikan: I adore Rin, it's thanks to her I found out I'm a loli fan. (No turning back now lol) Having read the manga, I know there is easily enough material for another 26 episodes. I just hope it gets done even though the manga is close to breaking laws at times =P
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Mahou Shoujo: Mahou Shoujo Lyrical Nanoha StrikerS: I would have picked Madoka but I've already put it down as a category. However in second I would definitely say this one. I loved the new additions to the cast and the abilities were pretty awesome. Some were fairly unique too.
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Mecha Code Geass R2: Yep, an obvious choice for me as I dont like Gundam. I loved this series and some of the Mechs were really well done...if not a bit OP.
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Feel free to add any genre I might have overlooked as I'm sure there are some I have left out.

Technically Seinen and Shounen are target demographics instead of genres, but whatever. More changes to appreciate different shows. And yes, Madoka is most definitely a seinen. Magical Girl shows are usually targeted toward kids... with older males as a periphery demographic. Madoka on the other hand is made specifically for the latter demographic.

Action: Yu Yu Hakusho - My genre best because the characters are all great (except maybe Keiko/Kayko), and the fighting is a step above DBZ's flash steps and energy beams.
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Comedy: Shinyraku! Ika Musume - Ika and her hilarious incompetence, Sanae's creepy stalker moments. Always amusing.
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Romance: Toradora! - Agreeing with this one. Not one single moment was boring. Love the development on Taiga, in that she actually has a reason for being so tsundere, instead of just "because people like tsundere".
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Harem: - Tenchi Muyo. Though I like it more for the comedy. Harem's not my cup of tea.
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Shounen: Digimon Adventure - Nostalgia and great characters with the most minimal flaws among the franchise. And it doesn't have the irksome filler of shows like DBZ, Naruto and Bleach.
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Mystery: Higurashi - I read the entire tropes page and I still got confused. Loved the characters. It was dark, a bit depressing, but not so overpoweringly depressing and hopeless that you don't care what happens to the characters.
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Slice of Life: Nichijou - Slice of life isn't my cup of tea either, but crank it up to eleven and throw in comedy and it made my Saturdays awesome for 26 weeks.
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Seinen: Yuru Yuri - More slice of life + comedy. This time with fourth wall jabbing yuri fun.
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Mahou Shoujo: Cardcaptor Sakura. The action feels more real than the conventional Magical Girl stuff, the characters are all lovable and even the unusual orientations are done tastefully and heartwarming enough to want to support them.
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Mecha Tengen Toppa Gurren Lagann. I've said it before, I don't like mechs, so imagine my surprise when I ended up liking this hot blooded awesome.

This is a good idea!

Action : FMA: Brotherhood. I don't even need to add anything more.
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Romance: Nodame Cantabile. It's pure love, it's set in a musical world, Nodame is just absolutely hilarious, Chiaki is a male tsundere, and it's Josei. What else can I ask for?
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Harem: Well, Ouran is a reverse harem, so I'll count that. It's hilarious and extremely entertaining to watch.
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Drama: Oh, this is hard... One of my favourite genres! I'll go with NANA. My heart hurts just thinking about it.
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Shounen: Hmm. Bakuman counts, right? It gives great background to the manga world, and it's so interesting to actually see how hard it is to make it big with manga.
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Mystery: Monster omgomgomgomgomgomgogomgomgomgomg. It literally rocks my socks off. Like, my socks just flew away because this anime is so flipping good.
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Slice of Life: I usually don't care for this genre at all, but Clannad season 1 was pretty SOL-ish and I really liked that.
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Seinen: I think Baccano is one, so I'll go with that. The plot was pure genius, and the execution was so unique. Of course, Isaac and Miria stole the show, but many other characters stood out as well.
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Horror: Hmmmmmmm. I've never watched a proper horror (except Another which was decent), but Jigoku Shoujo comes to mind. I think it's really underrated. I loved the eerie-ness of it, and how each episode was stand alone and they all have extremely tragic stories in them. Weird, because I usually hate episodic anime.
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Sports: Well, I haven't really watched a "proper" sports anime, although One Outs is on my PTW and I'm sure it'll be great. Can I say Hikaru no Go? It's the game genre, but I think game and sports is pretty similar.
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Ecchi: B Gata H Kei. I just loved that anime, which is weird because I am not an ecchi fan whatsoever...
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Mahou Shoujo: What else but Madoka? Yup, second favourite anime of all time. I remember I ran screaming into my brother's room after watching THAT infamous event.
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Mecha: I gotta have my Code Geass. I think it's a love it or hate it anime. It's one hell of an entertaining ride, through season 1 and 2 (although personally I think 1 is better). Too bad CG had such hate-able characters. Cough Suzaku cough.
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Sounds fun.
You didn't specify if Anime or Manga so I'll just list whichever.

Action: Sword Art Online. So addicted to it and its' MMORPG-esque setting only makes it better.
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Romance: Toradora. Unlike many, I very much enjoyed the last few episodes.
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Harem: Boku wa Tomodachi ga Sukunai. I dislike harems in general but this one I simply liked. There's no particular reason.
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Drama: Has to be Clannad AS. Tears were shed and I can't remember of anything else that tore me apart as much as this one.
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Shounen: KHR. Rings give you colorful flames and incredible power boosts. How awesome is that.
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Mystery: Not having watched much of this, I'll have to go with Gosick. Fun moe loli solving mysteries here and there.
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Slice of Life: Ore no Imouto ga Konnani Kawaii Wake ga Nai. While I think this is a hit or miss series, I instantly fell in love with it when I saw Kirino. Over time, that love transferred on to Kuroneko. Now I eagerly await S2 for more black cat.
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Seinen: Ef - A tale of memories. Probably because I haven't watched all that much Seinen.
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Horror: Never watched one. Hate the genre
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Sports: Barely checked any but Kuroko no Basket taking the spot right now. It's a fun, unrealistic basketball show/manga. It's got me interested.
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Ecchi:Kore wa Zombie Desu ka? While I dislike ecchi, this one's funny enough to make it all worthwhile.
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Mahou Shoujo: Madoka. First magical girl show I've watched, simply because it was different.
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Mecha: Code Geass. T'was fabulous.

Action: Katekyo Hitman Reborn. Nothing much to say
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Romance: Toradora! perfect romance+comedy anime.
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Harem: Clannad, the girls were obviously in-love with Tomoya
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Drama: Clannad After Story, even if I'm a guy, I really cried watching this (seriously).
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Shounen: Katekyo Hitman Reborn. I watched a few episodes and I liked it.
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Mystery: Another, I never guessed right who was the dead person there, which made it mysterious.
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Slice of Life: Ef - A tale of melodies. I somewhat related myself to the story.
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Seinen: Boku wa Tomodachi. this is seinen right? hehe
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Horror: Another, random mysterious deaths hahaha! pretty much enjoyed it!
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Sports: Slam Dunk, even if this an old one, I really enjoy this especially when Sakuragi's play surprises everyone.
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Ecchi: H.O.T.D. this is ecchi right?
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Mahou Shoujo: Rental Magica. Showed different types of magicians and LOL! Alchemy beats Sorcery.
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Mecha: Code Geass 1 and R2, Awesome knightmares and technology, pretty much what I want to make.

Action: Fullmetal Alchemist: Brotherhood. It should be self explanatory, the anime is only a known masterpiece.
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Romance: Kimi ni Todoke. This series to me was the masterpiece of romantic anime. It is a gem that shines brightly in this genre and is well worth watching.
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Harem: School Days. Most people would probably consider this to be one of the worst for the genre, but I highly beg to differ. I think that it is a refreshing change from the countless lighthearted happy fluff harems. Honestly, after a couple of them it starts to feel like you've seen them all. While they are still enjoyable if you like romance, I feel that the best of a genre should be one that stands out a bit more over the others, but this is a matter of opinion. What I like about School Days is it shows the consequences of cheating and hurting people. I'm quite the conservative person and feel like you should only give yourself to the person you're sure you love and are prepared to commit to for a very long time if not forever, if you don't then quite frankly you're the worst. So yes, seeing one character get extreme punishment for acting like a disloyal pig and seeing how the people he really hurt ended up was good to me. I think this series teaches a good lesson and has good moral values underneath.
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Drama: Kanon 2006. While I'm quite biased towards Air, Kanon has a better storyline. I prefer both Kanon and Air over Clannad and feel they are both worth checking out for slice of life/romance drama genre.
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Shounen: Hmm, Mirai Nikki. It has an incredible plot, the majority of characters are fantastic, and is also apart of the amazing psychological genre. The only thing I dislike is the ending, but it's good enough to not change my opinion.
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Mystery: Higurashi no Naku Koro Ni / Kai: Combination of both seasons as the mystery isnt complete without both. The first season had me guessing all the way and the second answered all my questions wonderfully. [2]
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Slice of Life: Hanasaku Iroha or Ano Hana, it's a tie for me. Hanasaku Iroha is one that falls under a bit of a cliche in anime, but still manages to shine. It has a good setting, all the characters are good and interact well together, and the plot developments are pretty good. Ano Hana also has a good setting, great characters that interact well together, and good plot development. The ending is also fantastic and very emotional.
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Seinen: Meh, I'd actually have to sit down and think about this one. I suppose I'll just go with Ef - A tale of memories since it is a good series.
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Horror: Jigoku Shoujo Futakomori. I think Jigoku Shoujo is a really good series. Contracting with hell to send a bad person there now at the cost of having to go to hell when you die, it's something interesting to watch and see all the different situations that push people to such limits. The second season is a bit better than the first because in the first season every single episode had the same layout to it. It was a rinse and repeat with different people and a different situation every episode, while season two mixes it up a little bit and makes it more enjoyable to watch.
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Sports: lol sports. No comment.
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Ecchi: I don't really like Ecchi that much, but I suppose I'll go with Sora no Otoshimono. I was able to really enjoy this series and it is the first "Ecchi" that comes to mind.
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Mahou Shoujo: Mahou Shoujo Madoka Magica or Cardcaptor Sakura, another tie for me. These two series are kind of like two different sides to the same coin for the magical girl genre. Both of them are really fantastic animes with good characters and strong plots, but one is very light and happy whereas the other is dark and quite sad.
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Mecha Code Geass. Another one that should be self explanatory.
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Action: Black Lagoon: Black Lagoon is the distillation of every Hollywood action flick ever made and then it is cranked up to the eleven, and at the same time is interspersed with philosophy, and contains numerous homages to other media (war films, Yakuza films) and contains amazingly surprisingly mature subjects such as terrorism and child abuse. And it has a cast like a Tarantino film, and unlike so much of modern anime, it actually has strong and competent female characters who don't break down all the time and need a male shoulder to cry on, and at the same time this anime contains over-the-top hilarious moments and at the same time features moments more mature than ten dozen Claymores and Narutos [with it constantly throwing at you info about the cold and harsh facts of life and shows the cruel reality of life behind the scenes in the underworld]...that and it is full of the single best gun-fights in the world of anime. As always, the awesome Madhouse Studios does not hold back on the budget and uses perfect and excellent use of music and lighting and backgrounds to make your blood boil and feel the action yourself. And not only that, but it is also a parody of itself at the same time hen all the above is happening. It makes fun of the action cliches that appear in action movies/anime series and thus provides a feeling of self-criticism that makes it a very honest series.

The characters are awesome in this series, besides their bada** ways and firing away bullets left and right, cursing, laughing maniacally in the face of the enemy, they also have a softer side and all of them get fleshed out in the course of the entire series. It is the perfect action series.
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Romance: Koi Kaze: Koi Kaze conveyed itself so well that you may even think about what you personally would have done in their situation.
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Harem: Bakemonogatari: Each girl had a great personality.
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Drama: Now and Then, Here and There You can actually feel their pain because of the depth and intensity of what is happening to them in this show.
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Shounen: One Piece It proves tons of fun with messages.
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Mystery: Ghost Hound The entire show is a a look at the human psyche with a basis in psychology, folklore, and religion. It focuses on what humans are, what memories are, the basis or emotions, and the nature of existence itself.
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Slice of Life: NANA Great Music, Realistic Characters, and great character designs.
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Seinen: Texhnolyze This is a series that only a Seinen watcher can love.
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Horror: Mononoke [The TV Series, not the Movie.]. For creeping me out all the time.
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Sports: Cross Game: Baseball and Romance? Yes
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Ecchi:Golden Boy Funny and Awesome.
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Mahou Shoujo: Princess Tutu For breaking the mold of the genre and using the Genre as a whole to create a masterpiece.
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Mecha : Neon Genesis Evangelion For changing the face of anime forever.

Action: Fairy Tail
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Romance: D.N Angel
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Harem: Hayate No Gotoku
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Drama: Vampire Knight
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Shounen: I already mentioned most the shounen I like in the other categories....but I guess I'll say Fairy Tail
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Mystery: Death Note
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Slice of Life: Kimi To Boku or Lucky Star
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Seinen: Acchi Kocchi
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Horror: Higurashi no Naku Koro ni
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Sports: I haven't watched any animes in this genre.
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Ecchi: I don't like this genre, but I guess any of the Zero no Tsukaima seasons...
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Mahou Shoujo: Shugo Chara
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Mecha : I haven't watched any Mecha animes.

Action: Jormungand
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Romance: Little Busters! Hasn't aired yet, but meh.
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Harem: Seitokai no Ichizon
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Drama: Clannad ~After Story~
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Shounen: Gintama
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Mystery: Another
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Slice of Life: The iDOLM@STER
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Seinen: Mahou Shoujou Madoka Magica
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Horror: Higurashi no Naku Koro ni
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Sports: Chihayafuru, apparently Karuta is a sport
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Ecchi: Kodomo no Jikan
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Mahou Shoujo: Mahou Shoujou Madoka Magica, I have not seen a lot of Mahou Shoujo
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Mecha: Mobile Suit Zeta Gundam

Interesting thread. Alright then:

Action: Black lagoon: In the Black Lagoon universe, your ability to get hit by bullets is inversely proportional to how awesome you are. The action was only matched by the dark and cruel environment the series sets place in.
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Romance: Toradora: Great comedy and characters that truly felt alive as opposed to most characters in a generic romance anime.
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Harem: Shuffle: This set the bar for harem anime imo. The love for the female leads towards the MC were as great as the disturbing backgrounds they hid of their pasts.
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Drama: Koi kaze: Is it love? Or is it merely infatuation? These questions tug throughout nearly the whole series. Let alone the moral problems it contains.
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Shounen: Yu Yu Hakusho: Spirit Detective, no other words need to be said. If you have seen this whole series you know what i mean. If you have not, well, you probably won't understand how much that phrase and this series meant to anime fans, even if you watch it now.
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Mystery: Hyouka: This series is airing right now, but at this moment, it has the potential of being placed amongst the greatest of anime. It's refreshing mysteries, along with its slice-of-life feel is taking anime fans to places that have not been traveled to in a long time.
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Slice of Life: Working: This is an innocently fun story of odd coworkers and their time together. What makes this show so great is solely the characters that are in it.
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Seinen: Monster: I'm currently watching this and loving the harsh perspective of reality it is portraying.
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Horror: Devilman(movies): I really can't really think of any anime that were truly horror-esq, But i remember watching Devilman when i was little, and it freaked me out, was still good though.
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Sports: Hajime no ippo: While the boxing is very exaggerated (It is anime after all), it still stands true to the positive 'heart' aspect of it. The boxers are very enjoyable as well.
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Mecha: Macross Frontier: Both the Action and the love plots were intensely well done.

Action: Samurai Champloo: Action is pretty much all there is to it.
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Harem: Seitokai no Ichizon: Not really sure if it's a harem or not, at least Sugisaki tries his hardest to make it one
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Drama: Clannad: After Story: If you've seen it you'll know.
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Shounen: Naruto Shippuden: Don't care what people say, Shippuden is awesome.
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Horror: Higurashi no Naku Koro Ni: First 5 episodes are brilliant
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Mystery: Guilty Crown: The mystery is figuring out how this piece of crap ever got made.
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Slice of Life: Welcome to the NHK: A Slice of Life anime that actually is just that, Slice of Life. Not cute moe girls eating cake.
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Seinen: Koi Kaze: So down to earth...
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Sports: One Outs: Yeah.
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Mecha: Code Geass: Yeah x2
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Thriller: Death Note: Because it's the best

Action: Fullmetal Alchemist: Brotherhood: 100% exploited potential, since the beginig, to the end. Every episode had SOMETHING, there wasn't any episode which felt like filler. I watched it almost one year ago, and I'm still fascinated about it ;)
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Romance: Lovely Complex: Hands down, my totally favourite shoujo. I loved every single character of it, everything within story was realistic, girl wasn't some kind of beauty, and boy hadn't fall in love with her since he saw her - it took a long time, until they were together at least, and that's what I love about it.
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Harem: Clannad: I think it's obvious choice for many people. Every girl had an interesting story (especially Fuuko and Kotomi), development at "main route" was believeable too, so yeah - it's definitely worth watching.
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Drama: Bokura ga Ita: With LoveCom it's my another favourite shoujo. Interesting and really dramatic at some point. I wish they'd make second season with later story, which was shown in manga...
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Shounen: Naruto/Shippuuden: Hello sentiment! Nice to see you again. Yeah, I know it's very... Mainstream. But I love it. I love stupid fillers (some of them are so stupid, that enjoyable by some point), cool fights, epis soundtrack, somehow interesting plot and how many cliches are there. It will be probably always no.1 for me (Narutard mode on).
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Mystery: Death Note: Masterpice, nothing really to add... I've got manga version on my shelf, and it's like the Bible for me :D
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Slice of Life: Fruits Basket: The only minus - it was too short! I hope that story, which continues in manga is as interesting, as the one within anime. Cute, heart-warming, but really dramatic at the last episodes.
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Seinen: Elfen Lied: It's not really my genre, but that one is really in my taste. Great, bloody massacre, epic opening and moe girls. Why would you need more? Still, the best part is in manga version, I think.
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Horror: Higurashi no Naku Koro ni/Kai: I know that it's not 100% horror, especially Kai, but watching first season at night... Just wow, I was really trembling with fear, especially at Onikakushi and Watanagashi part. Pure awesomeness, since I'm a big horrors fan ;)
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Ecchi: Kiss x Sis: I'm not really into ecchi, but it was amazing! Cute and sexy at once, I think it's anime for both sex 15+ years old, I'm a girl, and I enjoyed it very much ;) Hope for second season!
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Mahou Shoujo: Sailor Moon Sailor Stars: Classic. Without SM, and, especially, this season, I wouldn't be into anime, so it's very precious for me. It had everything - timeless opening, characters development, epic fight, drama, love triangle, shoujo-ai moments, friendship overcoming difficulty, good yet sad and nostalgic ending... Masterpiece in this genre, I don't agree with people who says that Madoka Magika is best mahou-shoujo anime. It's really good, but not even close to Sailor Moon.
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Mecha: Tengen Toppa Gurren-Lagann: Epic, awesome, amazing - words to describe this anime. I haven't watched many mecha anime (well, only it and NGE to be honest), but it's in my TOP10 Anime favourites. Some people says that the last fight is exaggerated, but I was watching it with sparkles in my eyes.

Action: Baccano! There's nothing quite as delightfully violent as this. Always worth a rewatch.
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Romance: Spice And Wolf: I love Holo and Lawrence's relationship, the way they play off of each other and tease.
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Harem: Negima: Really, I'm more talking about the manga here, but nothing does harem quite as perfectly as Negima, they've got all the bases covered.
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Drama: In terms of Anime, I'd have to say SKET Dance. In no other show do I get more involved in the main character's drama.
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Shounen: One Piece: This is pretty much the genre defining shonen. There are anime that are shonen that I like more, but this is what defines the genre for me.
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Mystery: The Tatami Galaxy: Starts off very confusing until all the pieces come together and you realize how perfect everything is.
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Slice of Life: The Melancholy of Haruhi Suzumiya: I love the SOS Brigade and the adventures they go on.
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Seinen: Seinen isn't quite as well defined for me as Shonen. I guess I'd just say Baccano again.
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Horror: Boogiepop Phantom: I don't know why I like this one, mostly because I didn't understand any of it. Still, it was fun to be confide.
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Sports: God I don't like Sports. Can I just say Bakuman? It's like a sports anime but with manga.
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Ecchi: Boku Wa Tomodachi Ga Sukunai: Why do I like this series so much? It's all perverted jokes and horrible characters but something about it draws me in.
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Mahou Shoujo: Mahou Shoujo Lyrical Nanoha: I've only seen the first one, but it really interested me. I need to get around to the others.
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Mecha Tengen Toppa Gurren Lagann: Manliest anime ever.
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Shoujo Ouran High School Host Club: Wonderful shoujo comedy and drama.
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Adventure Kino's Journey: Because life if a journey.

Genres:/Themes

Action: Mahou Shoujo Lyrical Nanoha. Lots of epic battles between (mostly) cute girls with insane magical powers.
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Romance: Toradora! the chemistry between thre two MCs is simply amazig, and the show itself is quite good, too.
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Harem: Clannad. A classic that should be on anyone's list.
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Drama: Kobato. It's mostly comedic overall, but throughout the show, you just know that all is not right with cute little Kobato.
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Mystery: Higurashi no Naku Koro Ni.This show is pretty much how a true mystery should be: it doens't spil the answer right away, but leaves enough clues behind for you to figure it out yourself (assuming you don't watch the sequel for the solution)
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Slice of Life: Tamayura ~Hitotose~. This show was made to make you feel good and relax.
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Horror: Another. You can complain about the last two episodes all you want, but I loved the show and it gave a real feeling of suspense, like a good horror show should be.
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Sports: Saki. This was the first sports show I ever watched. And though I don't understand a thing about mahjong , seeing a bunch of school girls use ridiculous powers to almost cheat the system was never before so entertaining.
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Ecchi: Hen Zemi. This show goes really, REALLY far in showing of the weirdest fetishes one could have. And I loved every minute of it.
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Mahou Shoujo: Puella Magi Madoka Magica. Probably the best Magical Girl show I've ever seen. Also quite unlike most of the more 'standard' MG shows.
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Mecha: The only mecha show I liked is Transformers, even though a lot of people would probably consider it a cartoon more than an anime.
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Comedy: Acchi Kocchi. Even if it's still airing, this show is non-stop laughter from start to finish. Plus, the girls are inanely cute.
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Yuri/Shouji-Ai: Yuru Yuri A show about school girl lesbians that is also very funny.
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Adventure: Dog Days is pretty much the only show in this genre that I watched (and liked).
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Fantasy: Fate/Zero. It's that good.
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Supernatural: Bakemonogatari. Studio SHAFTs masterpiece, and deservingly so.
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Parody: Pani Poni Dash. Just watch it yourself.
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School: Azumamga Daioh.
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Music: K-ON!. Even though it's a bit... lacking in the musical aspect.


Demographics:

Shounen: Phi Brain; Kami no Puzzle. Some of the puzzles are ingeniously designed, even more so because people utilize them to fight death matches with.
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Shoujo: Card Captor Sakura the only one I can think fo from the top of my head.
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Seinen: Needless. This show is so over the top funny, it has to be in my list somewhere.
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Josei: Usagi Drop. Rin is cuter than anything I've ever seen before. And I think the show did well to portray the trouble a single man has to go through to raise a child, especially if it's not his own.


Did I forget anything?

Without thinking too much:

Action: Black Lagoon
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Romance: 5 Centimeters Per Second
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Harem: Nisemonogatari
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Drama: Phantom: Requiem For The Phantom
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Shounen: Fullmetal Alchemist: Brotherhood
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Mystery: Death Note
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Slice of Life: Clannad: After Story
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Seinen: Hard one. Texhnolyze
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Horror: Higurashi
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Sports: Haven't seen any yet, I think.
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Ecchi: Nisemonogatari
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Mahou Shoujo: Mahou Shoujo Madoka Magica
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Mecha: Neon Genesis Evangelion: The End of Evangelion
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I'll try my best to avoid doubling on a title. Also, just to note, these are not 'the best' on my list, they're my favorites of the genres. If you wanted the best, you could simple search genres and sort by ratings. Avoiding listing currently airing stuff.

*prepare for wall of text*

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Action: Full Metal Alchemist: Brotherhood: This might just be me, but the series itself has many genres, I found action to be one of its best brought out through the series, though it didn't have action every episode, when it did, it was enjoyable to watch and all the fights were enjoyable from start to end. I've always been more into my fantasy/super power type fights than serious gun fights and the such.
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Adventure: Legend of the Legendary Heroes. I was disappointed with how the show ended opening and with no chance of a continuation, still, I'd say it'd be my favorite fantasy adventure genre.
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Cars: Redline. Considering I haven't seen many car genre anime to begin with and eye-gasmed over Redline, it gets my pick.
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Comedy: Gintama no doubt wins this and would win multiple other genres for me. Rarely see anything as humorous as this series is and when I do, it loses by episode count, tenfold.
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Dementia: n/a
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Demons: Nurarihyon no Mago: Sennen Makyou. To be honest, kinda just threw this out since series listed with demons aren't usually strong it the genre itself, usually just having a character being a demon. Nurarihyon no Mago uses the concepts of demons and their what their known for in the series. Now if Ga Rei had a anime, not Ga Rei Zero, it'd be my choice.
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Drama: Ano Hana. Made me cry. Nokemon. Secret base. Everything about it.
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Ecchi: This is tough, I have a lot of 'ecchi' genre shows I enjoyed. I guess I'll have to go with Highschool DxD. Not only did it have a decent plot, fucking mind-blowing for a ecchi, the fanservice in it was top tier. Fetishes? It does all mines.
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Fantasy: Soul Eater. Though fantasy isn't its strongest genre and the ending being crap. I still enjoyed it for its fantasy elements. Witches, werewolves, demons, etc. and for those 'which anime world would you want to go?" I'd chose this shows world because it itself is a shounen fantasy.
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Game: Yu Gi Oh 5Ds. Card games on motorcycles.
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Harem: To-Love-Ru. Specifically speaking, Motto and Darkness. The first one was pretty meh but after that, awesomeness harem ecchi.
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Hentai: Eroge! H mo Game. Most enjoyable hentai ever.
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Historical: n/a
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Horror: n/a. I've seen plenty of series with horror as a sub-genre but not strong enough for me to put it as a favorite horror. I usually avoid the series with horror as a main theme.
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Josei: Chihayafuru. Considering I only have like 1~3 josei in my entire list and the fact that I loved this show to the point of never skipping the opening even once, I can say it works. Sadly, I don't have much interest in its manga as it lacks what the anime has; animation, music and colors to go with the emotions.
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Kids: Digimon: Bokura no War Game. This movie... I still love it every time I watch it. The final countdown scene is embedded in my memories forever since I was a child. I actually found the English version more enjoyable than the Japanese version, maybe it's just because it more nostalgia.
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Magic: Negima!?. The one by Shaft. I loved its randomness thanks to Shaft producing it and it still kept the same concept of magic for each character even though it followed a separate story. Who else could have made a show revolving around chupacabras?
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Martial Arts: Kenichi. The beginning of the series I enjoyed it very much, only because it was somewhat more along the lines of more realistic... then it kinda turned superpower wtf hax over 9000. Well I didn't mind overall, I still enjoy the series.
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Mecha: Eureka Seven. Though others will definitely disagree, it's one of the most unique mecha genre I've seen that doesn't consist of constant mecha fights and repeated beam shots. Also being a shounen with an actual romance ending is a great plus. Music and animation were great to look at and listen to.
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Military: n/a
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Music: Perfect Day. Just a short music video by Supercell.
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Mystery: Mushishi. I just finished re-watching this for another time and still enjoyed every episode.
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Parody: Hayate no Gotoku. Duel hitsuji. Plenty of parodies and references that I actually understood.
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Police: n/a
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Psychological: Welcome to the NHK. I can relate so much to the characters... but I'm pretty sure that's not exactly a good thing.
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Romance: ToraDora. My only memorable anime that actually stood out in terms of romance. Yea, I don't really watch much series strong in the genre.
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Samurai: Sword of the Stranger. Best animated swordplay in anime history is it not? With great music to go with it.
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School: Seitokai Yakuindomo. School consisting of the most perverted girls and the student council president being the top tier of perversion? What school would be better than that?
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Sci-Fi: Steins;Gate. Being one of the top ranked anime can pretty much say everything needed for me. Though to add, it being one of the few sci-fi genres that I've seen that doesn't revolve around all the 'advanced technology Earth will probably never have in the future' and mecha/space.
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Seinen: Baccano. First of all, it being a seinen that doesn't 'revolve around high school / little girls'. Second, the great variety and cast of characters. Last, not your generic every day anime. Also to note, its English dub is superior.
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Shoujo: n/a. I can say I've seen plenty of shoujo but none that I favor.
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Shoujo Ai: n/a. I'd throw Shoujo-Sect in here but it'd be more suited for Yuri which I already have taken.
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Shounen: D.Gray-Man. Although the anime ended early, and the series itself is fairly generic in terms of shounen, I still favor this series the most compared to everything else. Mostly because of Allen's Crown Clown. I like how it looks.
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Shounen Ai: n/a
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Slice of Life: Nichibros. I would have put this in comedy, but Gintama took that spot. Though what this show also did great was doing what it set out to do, it's title. The daily lives of high school boys, just the characters enjoy their life in more of humorous manner and the series itself probably trolled us with a huge chunk of it being a dream.
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Space: n/a
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Sports: Air Gear. I'm not too fond of 'normal sports', I prefer the more unreal/fiction sports. Air Gear fits the bill using the concept of using motorized roller blades.
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Super Power: Eh, this one's kinda weird. Kinda hard to differentiate from Supernatural Fantasy elements/powers. I guess I'll just throw One Piece or something in it since it's labeled as it. I also find One Piece does it very well with so many different kind of abilities. It's so vast and gives out so much variety.
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Supernatural: xxxholic. Though its art wasn't the best, thank you CLAMP /sarcasm, I found it did the supernatural element pretty well with a mix of soft horror moments to it.
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Thriller: Madoka★Magica. Eh, I kinda just threw this here. I've seen multiple thriller genre'd anime but I can't say they were really 'thriller-ing' enough for me to favor it as a thriller. Madoka just had me going wtf multiple times.
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Vampire: Bake/Nisemonogatari. Though I wouldn't say the series is best fitted as a 'vampire' genre, the reason I did enjoy the show a lot more was for Shinobu, the vampire.
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Yaoi: n/a
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Yuri: Sono Hanabira. Cute and vanilla yuri. Nothing to hate from it.
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Action: Darker than Black
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Comedy: Hayate no Gotoku
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Music:Beck
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Romance: Kimikiss Pure Rouge (I usually like the romance secondary)
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Harem: Isekai no Sekishi Monogatari
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Drama: Kimi ga Nozomu Eien
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Shounen: Zero no Tsukaima
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Mystery: Mushishi
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Slice of Life: Clannad: After Story
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Seinen: This is difficult to say, I guess Salaryman Kintarou
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Horror: Elfen Lied
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Sports: Cross Game, with any doubt
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Ecchi: Kisxsis, I loved the poor guy trying to avoid the incest, the best that's been done.
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Mahou Shoujo: Claymore maybe...
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Mecha: Mobile Suit Gundam Seed
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In addition to this, a number of other categories aren't genres - it's a mix of themes, settings, fetishes, and so on. Ah well.

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Action: Rurouni Kenshin
This also has many genres to it. But the action reigns supreme. The fight between Kenshin and Shishio will always be one of the better fights I have ever seen in my lift.
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Adventure: Kino no Tabi: The Beautiful World
To me, this IS the adventure genre rolled up into one wonderful anime. I love watching Kino interact with everyone in the countries, I love the detail put into this anime. I just love this anime.
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Comedy: Gintama
Big surprise I know lol. Yeah I've changed my summary in my anime list from a basic synopsis to listing the episodes that almost make me pee myself.
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Demons: Kyo Kara Mao:
They're sorta demons! One of the few synopsis that have made me get funny looks I'm laughing so hard. Truly a good watch if you don't mind some slight boy/boy.
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Drama:Grave of the Fireflys
I have seen this movie a number of times, and I STILL go through at least five tissues while watching it!
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Ecchi: Highschool of the Dead
I don't like Ecchi but I do like zombies and the zombies in this one were golden. Loved it for the zombies, tollerated it for the boobs.
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Fantasy: Hakuouki
Fantasy unfortunately isn't a very well represented genre. I chose this one because it has touched me a few times and I really like the characters.
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Harem: Hayate no Gotoku!
Love the narration and the main character in this one is likeable and sweet.

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Reverse Haram: Fushigi Yuugi
This could have worked for fantasy also but, meh. Back in the day, I had a huge crush on one of the characters.
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Hentai: Golden Boy
ROFL so funny
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Historical: Hundred Stories
Also know as Requiem From the Darkness.

Horror: Higurashi no Naku Koro ni
Another would have worked too but oh my love for this show.
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Magic: Zero no Tsukaima
Love Louise. Funny chick. This is also a haram.
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Mecha: Full Metal Panic
Love this. Couldn't think of where else to put it lol.
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Music: Kiniro no Corda: Primo Passo.
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Mystery: Detective Conan
LOOOOooooooooooooonnnng but good. I have no hope of ever catching up though!
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Psychological: Paranoia Agent
My favorite WTF anime.
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Romance: Kodomo No Omocha
Maybe you will disagree with me, but I just loved the couple in this.
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Sci-Fi: Trigun
I named my pet fish "Pat the fish" after Pat the cat.
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Shounen: Fullmetal Alchemist:
Very Awesome.
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Slice of Life: Nichibros. I would have put this in comedy, but Gintama took that spot. Though what this show also did great was doing what it set out to do, it's title. The daily lives of high school boys, just the characters enjoy their life in more of humorous manner and the series itself probably trolled us with a huge chunk of it being a dream.
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Space: Mugen no Ryvius
Very Dystopic. Very cool.
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Super Power:Dragon Ball Z
Eh, why not?
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Supernatural: Natsume Yuujinchou
I can't say enough nice things about this series. This is my favorite all time series, I love the manga, the seasons just kept getting better. Definately give this a whirl!
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Thriller: Gankutsuou
Based on a classic tale of revenge, this anime is a peice of art - both in the story and the animation.
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Vampire: Vampire Hunter D.
Sometimes, the classics are the best.
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Yaoi: Sekaiichi Hatsukoi
Love this. So glad they are doing another series for this! If you are into Yaoi, check this one out!
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