Depends on the game. For singleplayer ones, I prefer to listen to the music developers included in the game. If a game is a little work of art, it is important to appreciate how sound adds to the experience and immersion. For example, the post-apocalyptic world of Fallout (more recent parts) would loose some of it's charm if it did not have a radio station with classsic songs you could listen to while hunting super mutants or running from Deathclaws.
But when it comes to multiplayer shooters, I do not listen to the music, as it disturbs me from speaking to my teammates.