Everybody's suggesting Samurai Champloo and Black Lagoon, it seems, and everybody's right. (Especially Champloo; it's not quite on Bebop's level, but it's a great ride nonetheless.)
Other stuff that's less like Bebop and Trigun but still worth checking out:
Gurren Lagann: About as ludicrously awesome as giant robot anime can get. Every time you think, "Okay, they can't possibly go any farther over the top," the creators smack you in the face with still more ridiculous badassery. The final episode is possibly the last giant robot-related thing anyone needs to make--it's just that awesome.
Berserk: An adaptation of the good part of the manga. Nice dark fantasy.
Evangelion: The series has its ups and downs, but it's pretty essential just from an anime education standpoint. The first of the movie remakes, "You Are (Not) Alone," is out on DVD in the U.S., and it's actually a substantial improvement over the first chunk of the TV series, I think--more streamlined and a whole lot better looking.
FLCL: This. A thousand times this. The definitive coming-of-age sci-fi comedy. And it has an unbelievably kickass soundtrack.
Azumanga Daioh: About as girly a show as I can admit to having fallen in love with. A great cast of characters and a charming sense of humor.
Paranoia Agent: A great, weird, wickedly funny thriller.
The Castle of Cagliostro: Great adventure flick by Hayao Miyazaki (Spirited Away, Ponyo).
Millennium Actress: A wonderful, tearjerking drama.
Post edited April 06, 2010 by PaakType