This is somewhat obscure, and not so cheesy, but the wonderfully rude British comedy The Young Ones had musical guests in almost every show, from Madness to Motorhead. One I’m especially fond of is the fun Amazulu (though they didn’t do my favorite song by them, “Cairo”).
I also liked Rip Rig + Panic’s appearance too, even with a different singer. The usual lead singer for RR+P was Neneh Cherry, (years before she came out with the now-dated but still relevant “Buffalo Stance” and (my favorite by her as a solo artist) “Manchild”) though the singer in that particular clip is Andrea Oliver.
Now I’m going to be remembering and chuckling at Young Ones lines.
Not as himself, but David Bowie did the voice for Lord Royal Highness in the extended length SpongeBob SquarePants episode “Atlantis SquarePantis”. The character had one green eye and one blue eye, playing off the popular belief that Bowie has two differently colored eyes (not true–his eyes appear different because one pupil is permanently dilated due to an injury).