Only game I remember was one that came out for the Commodore 64 back in the 80s called Rock Star Ate My Hamster where you had to put together a band, manage them (Publicity, tours, etc) and get 4 gold records within a year to win.
All the band members you could pick from of course were all parodies of the 80s most popular musicians at the time (and some from the 70s)