Well, I tend to like the more thoughtful stuff. Actually, stuff like Naruto and Bleach tend to really annoy me, because they're what people see most often, but they're so unrepresentative of anime as a whole. But when you watch a good anime, it has deeper themes than I've been able to find anywhere else. Unlike a movie, anime has the time to develop itself thematically, as well as adding depth to its characters and plot, so it's got the room to do a lot more with. And, even though western shows could do this if they wanted, they generally choose to avoid deeper themes, even if they do have character development, and occasionally some semblance of a plot.
The point though, is that you'd never find something like Ergo Proxy or Serial Experiments Lain in any other medium. American television isn't interested in investigating the arguments between deontology and utilitarianism, examining the complex natures of the psyche, or looking deeper into the relationship between a creator and his creations. And while American films occasionally decide to explore deeper themes like these, like I said, you simply don't have as much time to develop these types of things in a film, so the anime series still has something film simply doesn't. I'm not going to say that all animes have these depth (like I said, things like Naruto and Bleach annoy me simply because they are so devoid of anything but the simplest of themes), but you've got a much better chance of finding an anime series with depth than you do of finding depth in other filmic media.
