Juuni Kokki (Twelve Kingdoms): A withdrawn, unpopular do-gooder is drawn into a conflict in another world along with the school outcast and another classmate. There they become players in the revolution of one of Twelve Countries and eventually part of the story of each of the other kingdoms in turn. The music is lovely, the politics are complex, and the world draws heavily on Chinese mythology and the concept of "Divine Right" to rule. It starts out a bit overdramatic and is, unfortunately, incomplete (both in it's novel and anime formats)... but it's solid quality the whole way through.
BERSERK: A seinen series with a great deal of fighting, blood, boobs and guts. Oddly enough, it's also host to some of the most complex political and character interactions I've ever seen. Again... it's unfortunately incomplete and the anime is a bit dated: but it's a wonderful introduction to what's probably the best manga fantasy series ever written.
Rah Xephon: More or less a more subtle re-imagining of Neon Genesis Evangelion. A mech series with beautiful music, complex characters, amazing artwork and at least one episode that will bring even some of the blackest hearts to tears.
the films of Satoshi Kon (Paprika, Perfect Blue, Tokyo Godfathers, Millenium Actress, etc): A fabulous director for animated films that are both entertaining and thought-provoking.
There are quite a few more... but all the material listed here is more than worthy. No point overfilling the plate.