Anime
I haven't been into anime for that long but it is one of my favorite forms of animation. What I like most about anime is that it is animated cinema (animation that is "shot" like cinema). Anime makes its own distinct cinematic statement and that makes it very different from cartoons.
Here are some of my favorite anime series and oavs. Adjust your volume on the Escaflowne page.
Evangelion
Cowboy Bebop