I second the Cowboy Bebop recommendation. There are very few anime series that I have actually sat down and watched all the way through and Cowboy Bebop is one of them. The characters are compelling, the setting is surprisingly complex, and it has a comedic, episodic arch that becomes serial and dramatic arch halfway through the series. Also, the music is quite good as well; it is scored by a famous jazz musicial named Yoko Kanno.
The series is well done and full of surprises.
My other recommendation is Trigun, which I’m also surprised hasn’t made the list yet (actually, it may have and I’ve missed it–if so, I’m sorry). It’s about a man (Vash) who is a red trenchcoat-wearing vigilante who travels around helping people in a western-type, steampunk, post-apocalyptic world. It also starts as an episodic comedy series and then morphs into something more serious. It is less cohesive than Cowboy Bebop, but also has compelling characters and a complex, interesting setting. The music is also very good, and is scored by Tsuneo Imahori. The music sounds like a mixture of Vangelis from Blade Runner and Led Zepplin (if that makes any sense at all).
Both are worth checking out.
