A band i just started listening to is Yo La Tengo. They have been around for awhile and are i guess indie. But they have a large following and have lasted. There site is here http://www.yolatengo.com/

On the site you can listen to there music. Or click here for a short clip.
http://www.yolatengo.com/audio/yo_la_tengo_beanbag.mp3

Wikipedia describes them as a rock band but they don't really fit that category.

Meh, if you want to read about them. Check out the Wikipedia article
http://en.wikipedia.org/wiki/Yo_La_Tengo