(media list)
https://www.youtube.com/watch?v=tXeCLVsA5PQ ("Bonnie & Clyde," Serge Gainsbourg -> Luna)
https://www.youtube.com/watch?v=sDiFk0iXMoI ("Cheese & Onions," Spın̈al Tap -> Galaxie 500)
https://www.youtube.com/watch?v=LRsF1fQm3_0 ("No Quarter," Led Zeppelin -> Reggie Watts)
https://www.youtube.com/watch?v=37hJ6_yZhZ0 ("Dancing With Myself," Billy Idol -> Nouvelle Vague)
https://www.youtube.com/watch?v=ynDMqezSsbU ("The Black Page," Frank Zappa -> Pomegranate Tiger)
https://www.youtube.com/watch?v=wAkcSd5l9Qg ("Pictures of Matchstick Men," Status Quo -> Camper Van Beethoven)
(media list)
@zebratron2084 but no really actual covers:
Guns & Roses -> Postmodern Jukebox https://www.youtube.com/watch?v=JaAWdljhD5o&list=PL1A0956E790C7EBA2&index=45
Lady Gaga -> PJ
https://www.youtube.com/watch?v=VCTOpdlZJ8U&list=PL1A0956E790C7EBA2&index=55
Radiohead -> PJ https://www.youtube.com/watch?v=m3lF2qEA2cw&list=PL1A0956E790C7EBA2&index=54
A-Ha -> an orchestra https://www.youtube.com/watch?v=m3lF2qEA2cw&list=PL1A0956E790C7EBA2&index=54
Devo -> NIN (one of my longtime favorites) https://www.youtube.com/watch?v=W2M9jaulods&index=117&list=PL1A0956E790C7EBA2
in the Do Not Know If Counts category: Total Eclipse of the Heart, Literal Video version https://www.youtube.com/watch?v=W2M9jaulods&index=117&list=PL1A0956E790C7EBA2
(media list)
@zebratron2084 *cracks knuckles* I take it you're not looking for Weird Al-esque parody songs?
not sure if this one counts: Bassnectar remix of a Naked and Famous song (but I like it a lot) https://www.youtube.com/watch?v=1SN2GeDnZv8&list=PL1A0956E790C7EBA2&index=18
or this one: NIN got Gary Numan on stage to do "Cars" https://www.youtube.com/watch?v=cByGvnYxrng&list=PL1A0956E790C7EBA2&index=42
~or~ this: the song is the same, but the video makes it HILARIOUS (SAIL by AWOLNATION which is apparently ALLCAPS) https://www.youtube.com/watch?v=JaAWdljhD5o&list=PL1A0956E790C7EBA2&index=45