Some other choices I really liked on here:
Ghost in the Shell
Prince of Tennis
Naruto (minus the fillers)
Bleach (as was stated, not original, just awesome)
FLCL (fooly cooly is how it's pronounced)
I'll go ahead and add Outlaw Star and Trigun, both along the same lines as Cowboy Bebop.
Samurai Champloo (had a bad ending IMO, but a good anime overall)
A good swordplay one is Ruroni Kenshin.
I'm not big on Inuyasha, too much love story. If I want that I'll watch Eureka 7.
Death Note is an interesting one as well.
I also enjoyed sCRYed and a couple of the Gundam ones.
For those of you who do like anime and are looking for a great game with many of your favorites, I highly recommend you import Jump Ultimate Stars. http://youtube.com/watch?v=tlaJw_TUoTc That's an overview and review of the game. The only thing is don't listen to the guy when he says you need to know some Japanese. There is a full translation guide on gamefaqs. This is the best fighter ever made on a handheld IMO.
