Cowboy Bebop
FLCL
Mind Game
Memories
The Big O
Haibane Renmei
Mushishi
Kino's Journey
Kaiji
Princess Tutu
Ghibli movies, Porco Rosso in particular
 
Lengthier, less accessible but still great:
Revolutionary Girl Utena
Legend of the Galactic Heroes
 
The best of the best:
Boku no Pico