I think it depends on the situation. You've got games like Portal 2 thats use music and sounds together to set the mood and the pace like they would in a movie. Then you've got games like Amnesia: The Dark Descent that use music sort of in the same way, but it has a lot more time where there is no music so that the impact of the music when it occurs is stronger. Having no music for long periods of time makes you feel even more alone and isolated, which is very important for the atmosphere of that game. And it also enhances the impact of sound effects, which are very important in that game not only for setting the mood (letting you really hear Daniel's breathing when he's scared, hearing your footsteps echo in the hallway, hearing the building creek around you), but also for letting the player be aware of what's going on (hearing a growl and knowing what direction it came from, knowing what kind of a surface you're on, all the little sound effects that come from interacting with something).
Then you've got games like Limbo which sort of uses "sounds as music"--the steady and semi-rhythmic pulse of the environmental noise (the crickets chirping, the wind, bullfrogs in the swamp, etc) behaves like music, and only at critical moments does the game reveal any sort of true melody. It isn't actually music, but it has the same effect--it sets a pace and a mood through sound. Like Amnesia, the sound effects are enhanced by the subtle approach to environmental sound.
And then there's games like Bastion, which takes the total opposite approach--every second of that game is scored except the loading screens and significant narrative moments. This in turn makes the silence signify an important moment. Having music all the time sets the game to a regular tempo--it makes you want to play to the speed of the music. When the music is slow and solemn, you want to keep it slow and look around more. When the music is fast, you're in more of a hurry. It almost turns the experience into sort of an interactive music video--the music is playing, and what you as the player do is the choreography.
MMOs use music in a similar way--since players spend a lot of time in certain areas, the music sets a certain pace and atmosphere. Since the point of an MMO is to roleplay the gamemakers could get away with no music at all--and many do for lots of areas, but again having that background music gives the player that "interactive music video" feeling and makes them feel more heroic. Because the point of an MMO isn't just to give players a playground. The player wants to come from the experience feeling a little badass, so the game needs to deliver on that feeling.