Great Contest!
My favourite app for music is Slacker Radio, the biggest reasons being that the free version is very good, and it is offered on almost any device.
Fusion Music. It has a sleek UI, which has a really great feel and can edit song tags and stuff. It also has a lockscreen widget which I like in a music player.
Slacker Radio. I stream it while I do work around the house. It would be cool if i could use headphones so other people wouldn't have to hear the music also.