I'll echo the opinion that you need taste, primarily, but hey, I'm not here to judge. I'll name off some of my favorite bands with small descriptions for each. If you think they'd be something you're interested in, I'd recommend that you check them out.
The Go! Team
The Go! Team is concentrated energy funneled through a six-piece band and limited vocals. You can't help but be in a good mood after listening to them. Check out Keys to the City off of Proof of Youth or Junior Kickstart off of Thunder, Lightning, Strike to figure out if they're your thing.
The Flaming Lips
There's a reason this band's been around for 20+ years. You've probably heard one of their songs, even if you don't realize it. I really liked their recent album, At War with the Mystics, so you should check out Vein of Stars from that.
Wilco
I absolutely adore Wilco. Their sheer musicianship is amazing. Check out their latest release, Sky Blue Sky, and listen to Impossible Germany. Then go back and get Yankee Hotel Foxtrot and realize that, yes, it actually gets better.
Deltron 3030
They've only released one album, self-titled, but holy crap is it great. Even if you're not a hip hop person, this will get you into it. Be sure to check out the song Time Keeps on Slipping, as it actually inspired the conception of the next group...
Gorillaz
Basically the lead singer from Blur decided he wanted to pursue his eclectic taste in musical genres and threw a bunch of different stuff together, and it was great. They've released two albums, the first one self-titled (and containing a song you've probably heard before from some years back, Clint Eastwood), and Demon Days back in 2004. They've also got a bunch of EPs out and about. Be sure to check out the Soulchild Remix of 19-2000. It's great.
Muse
If you like Radiohead, but want a little more edge, then Muse is for you, because the lead singer sounds almost exactly the same as Tom Yorke. Pick up Black Holes nd Revelations. Knights of Cydonia is a standout track, but the truth is, every single song on that CD is great.
Anyway, that's a start.
EDIT: Oh, I forgot. Pandora.com is an absolutely fantastic site for people looking to expand their musical horizons. You basically type in a band or song you like, and it starts streaming a playlist of songs from other bands that sound similar. You can make a lot of great finds there. Also, if you know the name of a song that you want to hear, or a certain band that you just want to hear more from, check out Playlist.com. Both of these are completely free, so you've got nothing to lose.