Serial Experiments Lain
Texhnolyze
Akira
Millenium Actress
Haibane Renmei
Key The Metal Idol
Blame!
Now And Then, Here And There
My Neighbor Totoro
RahXephon
Neon Genesis Evangelion
Paranoia Agent
Kino's Journey
Kurogane Communications
Angel's Egg
Perfect Blue
Monster
Requiem From The Darkness
Darkside Blues
Elfen Lied (It's still growing on me, actually)
Spirited Away
Tokyo Godfathers
Saikano
Koi Kaze
Last Exile
NieA_7
Planetes
some episodes of Cowboy Bebop
The second half of Trigun (the first is borderline unwatchable)
Anything by Leiji Matsumoto (Galaxy Express 999, Captain Harlock, etc.)
Ghost In The Shell
the first volume of Ergo Proxy is awesome, and I'd be surprised if the rest of the series didn't follow suit
Boogiepop Phantom
Paprika (the new movie by Satoshi Kon, check it out)
FLCL
And other stuff. I know I've forgotten things (you see how I almost forgot FLCL there? Foolish!) but most of the critical stuff is in there.
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It's grime time.