It's pretty obvious to me now that it depends completely on what sort of game I'm playing and what I'm doing in it. I'm currently re-playing Star Ocean 2, and that game's music and sound effects get really tedious really fast, especially when you're trying to pickpocket the same people over and over, or level grinding new party members. Also, the voices in that game are just plain bad. So I tend to put on whatever music I want.
Same goes for puzzle games, or really any game where you're going to be hearing the same things over and over. The music tracks from Chrono Trigger and Final Fantasy VI are my favorites from any games ever, but at some point I just want to hear something else.
But if it's a game where music/sound are vital to the game experience, like Meteos, RE4, or what have you, then I definitely don't put on other music.