Foo Fighters (who may or may not be coming to town in their Chevy Metal guise, soon) have recorded dozens of covers the years, so many that they could do a boxed set of just covers. A lot of them match or even best the original.
Michael Jackson's "The Way You Make Me Feel"
Prince, like the Beatles, was/is fiercely protective of copyrights, so his material is near impossible to find online, so we'll have to settle for the Foo Fighters cover.
Jonathan Rado's cover