A lot of it, which is really strange because I tend to prefer Japanese games. Really, there's only a fistful of anime series I'm able to sit down and enjoy, and those are Cowboy Bebop, Ghost in the Shell: Stand Alone Complex, and Outlaw Star. I also have a general soft spot for Miyazaki these days, most especially Nausicaa of the Valley of the Wind, and there's an OVA called Karas that I recommend to any anime fans out there to check out. It's tough to follow sometimes, but it's a short, sweet OVA and things eventually come together in a way that makes some sense.
Everything else just... has problems, especially lately. One of the things that gets me is that I actually liked the grainier, more primitive animation styles from the 90's back a lot better than the cleaner digital work we see now--something about them just looked a lot more natural to me.
I kind of like Evangelion in that nostalgic kind of way and will never forget the impact it made on my early perceptions of anime and storytelling, but really, it wore thin on me after the first few episodes back when I originally watched it and it still does when I see it now. The characters are so obnoxiously depressing and melodramatic that I just desperately want to jump into my TV, punch them, ask Misato if Kaji is bothering her, and escort her quietly back into my own reality while everyone else resumes being a whiny *****, and then introduce her to fine pre-apocalypse rum.
Oh, but I kid. She's as obnoxious as the rest of them. ^_^
That really sums up a lot of my troubles with anime. I can't stand watching people be self-obsessed and whine incessantly when it seems to me like there's a clear course of action they could be taking and when it seems like the truth is plain as day. There's a kind of tension in experiencing a story like that, sort of the horror film-esque "don't go in there!" of social drama, but it's not the right kind for me, and it's unfortunately the kind that most anime I've seen seems to thrive on. I want to see room for doubt on both my side and the characters' if it's going to be there.
If it's not teen drama angst, though, it's just slow pacing that's my enemy. I really, really wanted to like Ergo Proxy, but it drags more than Return of the King. There's also a show called Monster. It's a mystery story centered around a surgeon named Dr. Tenma, who unwittingly revives a dangerous and methodical serial killer named Johann. There's no energy blasts or guns or big fight sequences here, just pure drama. It's surprisingly deft at crafting cliffhangers and nothing if not an incredibly complex and well-thought-out story, but if I recall it's over 30-40 episodes long, and it takes a lot of patience to get a good payoff out of it. If you can tolerate slower series, though, I recommend it, as it really and truly is a mindf*** of the finest caliber.
In the last category of anime I can't stand to watch, there's cutesy stuff. Haruhi Suzayaka or practically anything magical or cat-girl oriented or focusing on children either under the age of 15 or going to a school. Never mind the obnoxious go-nowhere uber-mindf*** plots, never mind that no human being I've ever met acts like these people do--I can put up with absurdity in the service of comedy. The voice acting is just painful to the ears. Shrill, piercing voiceovers and bad dialogue everywhere--and that's saying a lot, because I have to put up with Aisha every time I watch Outlaw Star, and let me tell you she's no treat to listen to in any language. It's that ludicrously energetic, overly bubbly tone that really puts it over the top, though. Bleagh.
That said, you should have an idea of what I like and what I don't like.
Apart from that, know that I completely dismiss popular tripe like naruto and bleach, which I understand essentially amount to one fight scene after another. There's only room for one Dragonball in my life, fellas.
Oh. One more I do like. Gurren Lagann.
You just can't hate Gurren Lagann.