Well, if you want some cool/innovative stuff, check out some of the following.
Menomena - they created their own computer program to mix their stuff; it's custom-designed for their music. They record their instruments, mix it up in the program, and then learn it from that, so all of their live performances are essentially remixes of their studio songs. They can be found here (crazy fucking site):
http://www.menomena.com/Thanks.html - click number 1, as it is a sample mp3. More can be found here:
http://www.cdbaby.com/cd/menomena
The Wrens home-record a mix of indie rock and emo. Despite emo's status as the most despised genre in many indie circles, even Pitchforkmedia (a review site) gave it a 9.5. Sample mp3s can be found here, though they don't do the record justice:
http://www.wrens.com/wrens/
Circulatory System is psych-pop that harkens back to the Beatles with a decidedly modern and philosophical twist. MP3's avialable here:
http://www.cloudrecordings.com/sights.html
The Notwist play indie rock with another twist: they have an electronic manipulator named Console who fleshes out their sound and glitches up the instruments. Very interesting. MP3s here:
http://www.cityslang.com/home.html - click MP3s, search the page for "Notwist." For these guys, only get songs off of
Neon Golden -- they used to be a hardcore band and only this CD is good.
So there's my basic introductory "interesting" band list. There are plenty more good bands, but those are good if you're feeling a bit adventerous. The good thing about them is they're all very accessible, but still have something thrown in to make them really unique and enjoyable.