Free GM Resource: Tabletop Audio
Tabletop Audio is a relatively succinct site that allows you to play individual 10 minute background sounds that are a mix of ambiance and music.
The cool thing is that it plays right in your web browser and you can even queue up a collection of sounds. Using the playlist is super simple and doesn't require much of your attention as a GM.
I realize that this site won't be for everyone, but it really doesn't get much simpler when it comes to playing some mood music for your game.