I played an IF (interactive fiction, or text-based) game a while back that used background sounds, like eerie chimes, and various situation relevant sounds. The sounds used provided ambiance that added incredible depth to the game.
Perhaps not necessarily music, but ambiance, like sounds of items being moved around in a shop, might be something to consider?
Then again, in my mind, music has always been an integral part of RPG games. Music as simple as that in the venerable Ultima series is forever stained in the minds of many of its players.