"Supernaut" by 1000 Homo DJs (a Ministry side-project). Better than the original by Black Sabbath.
The legendary banned version of "Physical" by the Revolting Cocks (another Ministry side project). Better than Olivia Newton-John's original.
The Sisters of Mercy did a terrific cover of "Gimme Shelter." I'm not sure if it was better than the original, but it was very, very good.
And an obscure German punk/metal/hip-hop/reggae group called the Freaky Fukin Weirdoz does a great cover of Gene Vincent's "Be-Bop-A-Lula."