I started out watching Akira, GITS, 3 x 3 eyes, Neon Genesis Evangelion and Vampire Hunter D. I keep a look out for other such gems.
Generally I suppose its SF-orientated fare for me. I don't mind the bubbly characters as well. Not too much silliness please but sometimes, as in Tower of Druaga, I can get along with it!
I read SF by authors such as Isaac Asimov, Arthur C. Clarke and Philip K. Dick. Also Japanese authors such as Project Itoh, Issui Ogawa and Yasutaka Tsutsui, who wrote Paprika amongst other salmonella related things.
You might be wondering how that is at all relevant. Well, there are some perhaps surprising similarities in these mediums and influences and references can be seen in both anime and SF Books.
Recently I have been enjoying the Knights of Sidonia manga and also the Haikasoru series of books.