Trigun is the best. I have never shown it to a geek who hasn't liked it. Start there.
After that, branch out into different genre's, take a spin on the first few episodes of different anime. I recommend Baccano, The Black Blood Brothers, R.O.D., Azumanga Daioh, and Please Teacher (not Please Twins!)
You can also check out some of the higher rated animes on this list:
http://www.animenewsnetwork.com/encyclopedia/ratings-anime.php?top50=best_bayesian
Do not start with Naruto, Bleach, One Peice, Dragonball Z or any of those style of shows! you will burn out. The time required to get a real payoff from watching these shows is enormous, they are not good starting points. Basically, avoid any anime with more than 52 episodes. If you like anime, consider these shows later.
Edit: I can't believe I forgot to recommend Gurren Lagann! Great show, add it to the list of things to check out after Trigun. The first 13 episodes (I think, before the time skip is what is important) are amazing, and the after time skip episodes are pretty good too.