I'll second the recommendations for Cowboy Bebop, Ghost in the Shell, Planetes, Haibane Renmei, and Evangelion.
I'm also a huge fan of the late Satoshi Kon, in particular his first two films Perfect Blue
and Millennium Actress,
two films which play with reality and perception in service of entirely different stories. His third film Tokyo Godfathers
is much more straightforward, but also brilliant - a great Christmas movie.
His series Paranoia Agent
is also great, if not perfect (the layout of the story is a little weird).
Also a big fan of Masaaki Yuasa, who specialises in a very wild, chaotic, freeform animation style. He's to an acquired taste, but his work is definitely something you should experience for yourself at least once. Alas, most of his output - Mind Game, Kaiba
- isn't easy to get hold of legally on region one or two, but his series The Tatami Galaxy
is on DVD.
Personally, I prefer Mamoru Oshii's older stuff, prior to GitS - Angel's Egg,
the two Patlabor
movies, and especially, the second Urusei Yatsura movie, Beautiful Dreamer.
Even if you don't watch any other UY, trust me - it's fantastic.
is a good, understated series about a traveling Girl and her talking motorcycle, who pass through various societies.
And finally, Serial Experiments Lain
, a pioneering mind-screw series that will leave you baffled (and perhaps a little freaked).