I quite like anime, Mushishi is one of my favorites, also love Seirei No Moribitu, which is about a female warrior bodyguard who has to protect the son of the emperor and deal with a demon.
Kino No Tabe is awesome and sort of like Mushishi--a girl and her talking motorcycle travel to different countries and each of them is very different and has like a philosophical story or point.
In the sci-fi genre:
Ergo Proxy
Serial Experiment Lain
Toward the Terra
Dennou Coil
I like this girly one called Haibane Renmai about some schoolgirls with wings and it seems dumb at first but of course gets trippy and strange and there's something odd about the winged girls...
My most favorite of all time is Mononoke which is about a traveling medicine man/demon hunter. It's in the horror genre and is very very bloody and scary and absolutely gorgeous.
Other interesting arty ones: Gankutsuo, Le Chevalier D'eon (cross-dressing French revolutionary spies possessed by demons), Bakumatsu Kikansetsu Irohanihoheto (totally incomprehensible one about a troupe of actors and the Shogun period of Japanese history and lots of swords and political intrigue). Can't remember any others I've been watching recently.
My favorite anime blog is: http://www.iwanihana.info/ and I pretty much watch everything suggested on there.