This can go either way with a game. I find that playing most music actually detracts from a game as it becomes a distraction to the player. Especially if it has lyrical content. There is one source of music though that I find often may enhance my game. It is music that has already been created for games.
Video Game Soundtrack Music
I often will buy a video game because it is the special edition that comes with a soundtrack. I download that music on to my phone and give it a good listen. Often times these soundtracks are backing music. They are unobtrusive and just right for a roleplaying game. So it is this the style of music that I may have on in the background if I am trying to enhance my game. The most recent version that I like but have not used yet comes from the Sexy Brutale (a brilliant video game by the way).
This style of music is already designed to be in the background. It is also designed to enhance the experience. Due to this, I feel that it can be used well. Many people will argue it is actually just instrumental music I am talking about. It isn’t. Classical music can be just as distracting as lyrical music! Keep rolling!