Let me list all the anime I have seen so I have that on the table:
Akira, Fist of the North Star, Vampire Hunter D, Neighborhood Totoro, Kiki's Delivery Service, LA Blue Girl (first 10 minutes only -- turned it off), Princess Mononoke, Project A-Ko
That's the lot, unless I missed something minor. Never saw Pokemon or any of the others.
What do I dislike? (Note: not hate) I generally dislike the Big Eyes, Small Mouth look. I dislike oversized weapons. I got lost in the plots of Akira, Fist of the North Star, and Project A-Ko. I prefer linear plots, realistic motion (of these, fantastically displayed in Princess Mononoke), and a more realistic palatte (again, done well in Princess Mononoke). I loath (yes, I do say that) representations of little girls being raped by tentacled creatures; I also realize that is only a minor subset of anime, the hentai. Such "art" as hentai I find morally repugnant. Most other forms, however, I merely find outside my usual tastes, both as a form of art and as a style of story. I don't think this is entirely a Western versus Japanese matter, as I have read several of Kawabata's novels and Genji Monogatari and enjoyed them.
What about other animation? Well, I like Rocky & Bullwinkle, but obviously for the actual animation. I like the Pixar material -- the plots are great, the characters move in a very believable manner, and you have to love the voices. I never was a fan of Hanna-Barbera, other than briefly as a child. So I can say that animation in general is not quite my cuppa.
My taste in art falls firmly into the realistic school. I love the Flemish Renaissance artists -- Bruegel, the van Eycks, Bosch, Vermeer; going north, I love Durer and Holbein. I love Magritte who, though he creates odd settings, is highly painterly. I also have a deep love for M.C. Escher.
So there we go. You may decide that I have limited tastes, and I can respect that, but there is no need for me to like all styles of art.