Guitar Hero and Rock Band 2 introduced me to
Boston ("More than a feeling"), whose first album I loved. The others have good songs too, but their debut one is incredible.
RB2 also made me discover
Fleetwood Mac ("Go your own way"), thanks to which Rumours is now one of my favorite albums ever. Of course, they have a lot of other fantastic ones, such as Future Games, Bare Trees and Behind the Mask, but I'll never forget which song was the one that I first heard. Man, that game has a killer soundtrack that I didn't know before playing it:
"Shooting star" (Bad Company),
"Pinball wizard" (The Who),
"Rock'n me" (Steve Miller Band),
"Carry on wayward son" (Kansas) -I've barely heard anything else by the last two bands, I should fix that soon- and
"Everlong" (Foo Fighters), which at the time I didn't like and took me over 2 years to appreciate.
I also listened to the first two albums of Lynyrd Skynyrd thanks to
"Free bird", which appeared on Rock Band 3. So I can honestly say these rhythm games influenced me the most, and helped me add some gems to my music collection.
Hell yeah, Perturbator is awesome!
"Miami disco" blew my mind, and made me hear the rest of his stuff.