Depends on the game. Mostly, for the sims I listen to whatever I have on my iTunes. It gets annoying when you have to listen to the same songs on the game. So, a bit of variety does the game good. Unless, the soundtrack is great, I don't listen to anything else. (Dragon Age, Mass Effect, etc at these types of games that fall into that category.)
I don't listen to outside music when I play video games usually. I enjoy the music the game has to offer most of the time.
Especially the Zelda games, the theme songs and the songs in dungeons make the game that much more enjoyable.
Sometimes I listen to some soundtracks of the game or anime. But sometimes I don't because I want to focus to what I'm playing.
I don't listen to music when gaming, I listen to the soundtrack that was made to be listened to while playing the game. People make a lot of effort to make game music and it's very annoying when people don't respect it.
The background music of the game. HAHA I feel like the mood and atmosphere is ruined if I don't listen to the sound effects and background music of the game. For example, LOL has many good background musics. Also, the "Double kills", "Triple kills" are the reason I don't listen to my own music when I am in a game.
I like Christian Music while playing, I don't listen much to secular because to me it's a bit meaningless and no offence to anyone who listens to secular.
I like listening to indie pop/folk or electronica when I'm playing League of Legends because it ups my focus and it doesn't distract me from the game. It's actually quite relaxing and most of the lyrics are catchy in a really subtle way when it comes to indie pop.
I usually listen to the chillstep because it relaxes me a lot while I'm playing and I love the feeling of peace and relaxation that thi music can give me.
I don't listen to music as much as I use to when gaming. But I usually listened to metal, r&b or techno music a while back, I think.