I enjoy all kinds of genre and would watch pretty much everything. I'm mostly drawn to action, adventure, psychological thriller, mystery, slice of life, and romance. I'm also a big fan of old school anime and series from the World Masterpiece Theater.
I have been watching anime since I was a child (around seven to eight years old I believe), albeit with frequent hiatuses over the years. The very first anime I've seen—if I remember correctly—was Blue Blink; but it was Rurouni Kenshin that really got me drawn to this particular medium. I'm more into anime than manga as you can see on my stats.
I don't really watch a lot of movies/side-stories or OVAs unless they are adaptations from the original material or if they are from series that I'm highly interested in. I also kind of have a habit of re-watching my favorite series.
MAL rating system sucks, so I made my personal rating scale, which is just a general interpretation of my scores that I use ONLY for all the anime that I saw.
Disclaimer: I'm not an anime expert and I'm not trying to be one. I just created this to make my rating a little more consistent.
Of course, this is all still subjective and like everyone else, I could be biased on a select few series.
10 - Pinnacle. The closest to a masterpiece I have ever got to see in anime. It is by no means perfect—but in comparison to other series, it is basically unsurpassed.
9 - Outstanding. Anime that I found to have a very compelling story and/or characterization. There is a masterful depiction of their themes and almost everything about them is memorable. I consider these shows to be the best in their respective genres (bar anything in the 10/10 area obviously).
8 - Great. Anime with charming and pretty solid story, execution and characters. Also highly entertaining or emotionally investing. The flaws are minor and perhaps one of the best in their genres.
7 - Very good. Still entertaining with intriguing and promising plot, but usually are lacking several elements that could have made them great. In some, the flaws are more evident, but are still overshadowed by their thematic charisma.
6 - Decent. Above average series in which the good aspects about it still outweigh the bad. I usually give this score to series that I either: didn't enjoy that much despite having a well-thought story (like Steins;Gate) OR did enjoy thoroughly despite having a rather flawed story (like Assassination Classroom).
5 - Average. My default score that I usually give to anime with the same amount of good and bad in them. There are some series here that I enjoyed more than a 6/10. There are also a few times when I could really be unsure what score I should give, especially when it comes to OVAs and specials, so I either just give them a default score or not rate them at all.
4 - Bad. Story is sub-par; the flaws outweigh the good things; characters are either bland or annoying. Still enjoyed to a certain degree.
3 - Legitimately bad. Almost similar to a 4/10. The difference is that I did not enjoy anything about them at all and only continued watching due to sheer curiosity.
2 - Horrible. Either poorly written or cringe-worthy series with very few redeemable qualities. Just only slightly more bearable than a 1/10.
1 - Bottom of the barrel. Series with no plot, just plain obnoxious. I would not recommend even to my worst enemies.
I try not to rate anime that I haven't completed unless I've seen enough (or at least more than half) to know where it goes. Ratings that I've given to unfinished series are only relative to the episodes I've seen, not necessarily for the entire anime. Sometimes, I'm unsure what score to give, so I just leave them unrated.
I also don't really take art/animation or music/sound into account when rating because neither really significantly affects the quality of the story or my enjoyment of the series unless they are extremely horrible. Not gonna dock off points from a solid, highly entertaining series just because the art or sound isn't pretty.
I rate anime based on:
Quality (story, execution, characters, pacing): I rate series based on the story's premise and how well it has been executed. I give high ratings to those that have interesting and/or well-developed characters. I also give points to those that are well-paced.
Note that I also consider the type of anime I'm rating, when it was made, and what it aims to achieve. Hence, I shift the weight of my rating amongst the aforementioned elements accordingly. For example, I don't rate anime like One Punch Man based on quality of story for obvious reasons since it does not really intend to tell an intricate story to begin with.
Enjoyment: This holds an equal weight with the above because this is the reason why I watch anime in the first place. There is no point in watching solely for negativity and criticism.
Completion: A good story has a proper conclusion. It doesn't have to be a close-ended one (i.e. open endings are fine), just that the major conflicts/plot points should be resolved and wrapped up by the end.
Obviously, I'm not expecting anyone to agree with me since we all have our unique preferences. I'm just putting this here in case anyone is interested on how or why I rated series the way I did.