This is for songs which have been remade by other artists. You don't necessarily have to say who did the original (heck, that might be more fun to make us guess!) but I want it to be a remake you LIKE.
So, for instance, Apocalyptica's version of Metallica's "Nothing Else Matters":
Apocalyptica gets an awesome! vote from me because of their version of David Bowie's Heroes.
Its sung, in German, by Rammstein's Till Linderman (who could read a phonebook and sell it and I'd buy it)
Laibach is also awesome for their covers/versions, like their latest album, Volk, which is the reworked national anthems of 14 countries. Here's Anglia, from that album-
Also google up their cover of Life is Life, One Nation, Final Countdown and Accross the Universe.
Edit: Do' oh! Someone's already posted the Johny Cash "Hurt" cover. So here's the Meatloaf version of Celine Dion's "Coming back to me now" (which technically isnt a cover, as Jim Steinman wrote if for Meatloaf after "I'd do anything for love", but the two got into a fight and he then sold it to Celine Dion)