-A solid story, typpiicaally leaning more toward shonen and coming of age type things, or like action fantasy sorta stuff. Not usually a fan of overly romance-focused plots or slice of life, tho there are exceptions.
-Good pacing and how it plays out its dramatic moments. This is pretty much the number one reason why I drop anime I would otherwise enjoy. Usually if it's rushed to the point where I feel the characters don't get enough screen time or development, or if they draw out every dramatic moment unnecessarily it's just... ugh.. I can't.
-Follow through on built-up story beats. It drives me up the wall when a plot sets up your expectations to follow through on certain things, and then never does.
-Well written and diverse characters with enjoyable interactions and relationships. I want to see depth, motives, personality quirks, growth. I don't like characters being there just to be there and serve shallow plot purposes, that makes them boring.
-Female characters aren't overly sexualized. I can put up with a little and there are exceptions if it's more comedy based (for example, I really enjoyed FLCL, TTGL, KLK, and No Game No Life) and if they have a really strong and interesting plot otherwise, but when it's stuff that doesn't really have any business sexualizing girls and does it anyway just for the sake of doing it, it's super gross and a major turn off.
-Good, fluid animation -- the looser and wilder the better. (No CGI pls jfldas)
-It doesn't get "too big for its britches." Not sure how else to put this, but when a story and the bad guys just get bigger and bigger and bigger to the point where it's like you've completely lost touch with the whole reason for the story to begin with. Naruto kinda did this in the end, and as far as I got into Bleach it definitely had this problem, too.
Some of my favorite anime include FMA (Brotherhood), Mob Psycho 100, Gurren Lagann, Re:Zero, Kekkai Sensen, Durarara, Monthly Girls' Nozaki-kun, Noragami, and Occultic;Nine.