Revolutionary Girl Utena: The level of symbolism is insane in this show. But a good insane. This show combines a highly developed cast, great art direction, and meaningful themes to create a unique masterpiece that will probably never be recreated.
Cardcaptor Sakura: This show means a lot to me, partly because I watched it during a hard time in my life and this show is perfect for bringing a genuine smile on your face. The characters are just so enjoyable and up-lifting. The art and animation are also great considering the time it was made! This is probably my favorite magical girl show.
Code Geass: This show (&R2) doesn't have the best writing, and it's plot twists can be over the top, but it was so entertaining that it's one of my all time favorites. Even with all the writing flaws I especially love the cast, and the main characters really stand out to me.
Rose of Versailles: A storytelling masterpiece! I've always been interested in Marie Antoinette and the French Revolution so this show was perfect for me. On a side note, during the middle of watching this show I took a trip to France and I actually saw the Palace of Versailles! They even had the Rose of Versailles manga in their gift shop.
Mawaru Penguindrum: Another Ikuhara show. Going into it I wondered how it would compare with Utena, and in my opinion it does! The first 10 or so episodes do seem to follow a semi-normal structure with nothing too unusual. But after that the levels of symbolism are insane. It's a really fun anime to analyze because the sheer amount of symbolism is so immense. I also loved the core themes of the show especially family.
Spirited Away/Ghibli in general: This is a more broad category since Ghibli films would easily fill a lot of my favorites so I just put them into this broad category. Spirited Away however would be my favorite of them all. It's hard to describe to sense of wonder you get from watching Ghibli movies, but it's hard to find.
Shinsekai Yori: This is one of the best dystopian anime that I've seen. I loved the depth of which their society was explained, and the intricacies of the plot were very cool. The only weakness I could find out of this show is that its main cast doesn't stand out that much, but the plot makes up for the that.
Neon Genesis Evangelion: When I first watched this show when I was 14 or 15 I didn't really get a lot of it. But once I rewatched it as a 20 year old I get it so much more, and I relate to several of the character's struggles. Speaking of the characters, this show has some well developed and unique characters.
Madoka: One of the best magical girl shows of recent times. This show had everything: it was concise, had brilliant art direction, strong themes, and an interesting cast.
Hunter x Hunter (2011): It's rare for me to watch an anime over 100 episodes, but this was an exception. There's something about Hunter x Hunter that makes it stand out in comparison to its peers. Also the Chimera Ant arc is easily one of the greatest arcs that I've seen. Watch it!