My all-time favorite anime is Tekkon Kinkreet/ Tekkonkinkreet. It's very different from typical anime. It's got action, it's got drama.
Art-wise, it is top notch; the animation is fluid, and the backgrounds very detailed and alive. However, the characters are NOT pretty/ handsome/ etc, so some people might not like that. I didn't mind it, personally.
Story-wise... again, top notch, and again, not for everyone. It starts out almost normal, then becomes more and more surreal as the movie progresses. Towards the end, it's almost all symbolic (nothing overly pretentious, though). My cousin who watched it with me compared it to EVA. Although EVA and Tekkon are very different from each other, I can kind of see where he's coming from.
Oh, and the English dub is actually good. @_@ I watched it first in Japanese, then in English. They're both great -- in fact, there are some parts of the film where I actually prefer the English dub.