I went looking for Madonna covers today. A lot of bands have done covers of a lot of her singles. Perhaps her most covered single, however, is "Burnin' Up", which was a very early single and her first minor pop chart hit.
So, when I stumbled upon Iggy Pop & The Stooges doing that song, as well as "Ray of Light." a later single, I had to jump on that. Sure, they aren't traditional covers of her songs, but Madonna - who is in attendance - seems to enjoy them.
A side note - Mike Watt, who has been a Stooge since 2003 and is on stage for this performance, also covered "Burnin' Up" as a member of the Sonic Youth side project, Ciccone Youth. (It is said that this project is what got Mike Watt out of his deep depression over the loss of his best friend and Minutemen bandmate d. Boon) Here is their version, with Watt on vocals and boom stick, and guest starring Greg Ginn (of Black Flag fame) on guitar.