A band called Old School Freight Train performed on an album called The Bluegrass Tribute to Air, which, although otherwise pretty terrible, had an amazing version of "Kelly Watch the Stars." I recently bought the same band's new album at Virgin's closing sale because I liked their version of "Kelly..." so much. Anyway, they covered "Heart of Glass" by Blondie and although I was cringing as I put the cd on, it turned out to be extremely well done (although the words are a little flippant for the somber arrangement they gave it). What other covers are there in radically different musical styles that turned out surprisingly well? Some I can think of: Goldfrapp, "Physical" [Actually this one is titled U.K. Girls (Physical).] Devo, "Working in the Coal Mine" Devo, "Satisfaction" Cat Power, "Satisfaction" Scarlett Johansson, "Falling Down" Cake, "I Will Survive" Nicolette Larson, "Lotta Love" Scissor Sisters, "Comfortably Numb" T-Sign, "Have a Cigar."
How about the Johnny Cash covers of Nine Inch Nails' "Hurt" or Depeche Mode's "Personal Jesus"? They were pretty good.
Daft Punk's version of Better Stronger.. I don't know if this fits in here but Kanye West did a terrible version of it.