Soft Cell's Tainted Love is so definitive many think it the original. I really like Marilyn Manson's cover, which twists it into something darker.
Korn's cover of the Wall is might fine, but doesn't stray far from the Floyd.
Placebo (a band I don't like) vastly improved Running Up That Hill, to the extent it's the second most played track in my music collection according to Itunes.