Mr.Deflok

In terms of traditional artwork I'd have to say Jin-Roh is a masterpience, the animation is so realitic and life-like you'd swear those are real actors you watch on the screen. In terms contemporary artwork involving CG you can't go past Ghost in the Shell, it's sequel Innocence and even it's series, Stand Alone Complex, they're all unbelievably good.

At the moment though Voices of a Distant Star is my favourite anime all round, great story, great characters and brilliant animation.

Serious anime has the power to make me cry, strangely, most film cannot (unless it's Kurosawa).

EDIT: You should also try out some of Hayao Miyazaki's work, my favourite being My Neighbour Totoro, no evil bad guys, just two kids, their imagination, love and fun, and again, I cried my eyes out during it because it was so beautiful (the tree growing scene is perfect).