I would recommend Neon Genesis Evangelion over pretty much any anime, it's still the most intelligent and fascinating anime that I've seen.
I really enjoyed the 2 Standalone Complex seasons for Ghost in the Shell, along with the movies. The 2 S.A.C. G.I.T.S. are even closer to the books than the movies.
Another scifi classic with a western twist is Cowboy Bebop, with it's amazing soundtrack (jazz !).
Right now I'm watching Mushishi, which reminds me a lot of Miyazaki's Mononoke Hime.
If you're into tales or mythology, Juuni Kokki (The Twelve Kingdom) is a very good show, heavily influenced by Chinese mythology.
Monster, adapted from the manga created by Naoki Urasawa, with it's intricate story and dozens of characters would be suited even for those of you who don't normally watch anime but enjoy psychological thrillers.
I also watch a few shonen, One Piece with it's universe full of wacky characters would be my favorite.
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