Additions:
The Miyazaki movies - including My Neighbor Totoro and Spirited Away
.hack series - a lot of people say it's boring, it isn't - those people just don't know how to follow a story

Reiterations:
Neon Genesis Evangelion
Bleach
Rurouni Kenshin
Trigun

meh, I guess I'd recommend Hellsing. Strange that I didn't like it for the one reason I loved Evangelion, though. (I seriously don't think that Hellsing answers everything.....) It's short, though. And the first few episodes weren't my thing. However, if you're into the whole... I guess I'd call it necrophiliac.... thing, the beginning is much better. (yes, I WOULD take out the first couple even episodes)