Well, I'm actually surprised this hasn't been recommended yet so I'll go ahead and do it.
Neon Genesis Evangelion, you'll either love it or hate it. Cool mechs (if you can call them that), awesome aliens (if you can call them that), and a cast of pretty messed up heroes (if you can call them that). And the story is pretty damn good, although definitely requires more then one viewing to understand. My only advice is not to watch the last 2 episodes and watch the movie (End of Evangelion) instead. Although I understand the original ending now, the first time it really bummed me out.
You can also give Rebuild of Evangelion a go. It's basically a remake of the series in the form of 3 or 4 movies, with a way bigger budget then the original show had and some pretty noticeable changes to the plot. So far only the first movie is out.
You can also give these a go: Angels Egg, Akira, The Wings of Honneamise, Vision of Escaflowne, Berserk, Perfect Blue, Hellsing (both the TV series and the OVA), and RahXephon.