Azumanga Daioh - It's funny, nothing too deep, and not too long either, it's great if you just wanna sit down and laugh at something.
Ergo Proxy - A sci-fi animu with a hint of psychedelic, delicious.
FLCL - It's so short that you can watch all the episodes together in one run as a 1½ hour movie, plus it's fun, about a boy who grows up.
Ghost in the Shell: Stand Alone complex (+2nd gig) - I really do enjoy a good sci-fi series, although with he 2nd GIG it almost gets too long for me, I don't like animu that's very long.
Gunslinger Girl - Lolis with guns. nuff said.
Paranoia Agent - a psychedelic series about a boy who turns peoples lives around by hitting them in the head, although it takes a turn when one of them begins to recall bad memories.
Serial Experiments Lain - This one is my personal favorite, its deep, and leaves you with loose ends until the last episode, that's number 13, as said I don't like long ones, and SE Lain manages to get a lot of stuff into 13 episodes.
Movies:
Cat Soup - a psychedelic adventures that makes you travel in time and space, in the desert and ocean, all in 30 minutes.
Ghost in the Shell - I'm just a GitS fan really.
Howl’s Moving Castle - This one is very rich in backgrounds, a real pleasure for the eye.
Innocence - moar GitS.
Kiki's Delivery Service - a cute little movie about a girl trying to find her role in the world in the business of being a witch.
I've seen more than those listed above, as I were a real weeaboo in my early teenage years, I still do appreciate a good animu, but nothing more than I would to a good western cartoon, but I didn't list them because they were a waste of MY time, too long, too serious, not serious enough, I'm very picky about what I spend my time with.