Some types of games like skateboarding and racing games have featured licensed music for a while now. Since people don't usually buy games based on or even with knowledge of the music in them, they seem a likely medium to expose people to stuff they haven't heard.
Recently, I learned to slightly tolerate Theory of A Deadman after playing Indigo Prophecy. Before the game, all I knew was they came from the same garbage heap as Nickelback.
But a game actually got me interested in one of my favorite artists. There was this PSX skating game, Street Sk8er, that had a song by Weston called "Liz Phair." Sort of a stalkery love ode to her and her songwriting ability.
"You look so pretty in your video,
And you write better songs, than anyone I know."
It was really the only thing I liked about the game, and I played it for a while just to listen to it. I didn't get in to Weston, but I wanted to see what he was babbling about so later I bought "Exile In Guyville" by Liz Phair and now she's one of my favorite female songwriters.
Also from a skating game, one of the Dead Kennedy's songs, "Police Truck," was in a Dreamcast Version of Tony Hawk's Pro Skater. That helped get me interested in them. Tony Hawk three had "Ace of Spades" in it, too, and that helped me get interested in Motorhead.
What bands or artists have you discovered through games?