Before I begin, let me assure you, gentle reader, that I am not actually and indie music guy. First, I don't have the build for it (I'm more Fat Joe than Bright Eyes), and Second, I consider music to be something nice to listen to while playing a video game, or writing a paper, or just fooling around. I don't consider it to be an integral part of who I am in relation to the world, if that makes any sense. I certainly enjoy a lot of indie music, but I don't spend a lot of time or effort keeping up with it.
That all said, my favorite band of the last four or five years has to be The Dismemberment Plan. Named after a throwaway line from Groundhog Day (when the insurance salesman is pitching Bill Murray), the D-Plan is nearly unclassifiable as a band. They get lumped in with emo, if only because they tend to sing about emotions and wear tight clothing. They released four studio albums, a couple of EPs and split sevens, and then "Poof! they were gone." Over those four albums, they progressed musically, shifting from anarchic indie pop that actually made you want to dance to lush, layered rock that makes you listen again and again. I'm sure I'll tackle each album in time, but for now, just be aware that they're one of my favorites.
They're website http://www.dismembermentplan.com/ has stuff you can listen to, download, etc. Check it out!