Highly unlikely this is possible with any system, mainly because of licensing reasons. The Guitar Hero developers have to get permission to use each and every song on the game, and also pay a percentage of the money made from every copy sold, to the music industry.
It doesn't stop people from creating their own custom versions, but you need a modified console in order to run those discs.
Assuming it were possible... Any system with a hard drive should, in theory, make it possible. So the 360, PS3, and Wii. It's just VERY unlikely to ever happen unless there's some sort of a fee associated with it.
Does anyone know if it is possible to download songs for guitar hero via your gaming system. If so, what systems allow you to do this and how do you go about doing it. I have xbox 360, ps2, and wii. Thanks