Marvin Berry & The Starlighters - Earth Angel (The Penguins)
Metallica - So what? (Anti-Nowhere League)
Satyricon - Orgasmatron (Motörhead)
Sepultura also made a cover of this song.
Not a cover either way but the song Motörhead is way way better with Hawkwind than with Motörhead, I think.
Satyricon - I got erection (Turbonegro)
Gnarkill also made a cover of it.
The Nutley Brass - Last Caress (Misfits)
Had to include the original, it's just not the same when you can't sing along. And the instrumental cover isn't better, few things are. But it's fun. IMO All Misfits covers ever made are worse than the originals, vocals can't be surpassed.
Also:
Paul Anka - Smells Like Teen Spirit (Nirvana)*
Pet Shop Boys - Always On My Mind (Elvis)*
Marilyn Manson - Tainted Love (Gloria Jones)
Manfred Mann - Blinded By The Light (Bruce Springsteen)
Metallica Am I Evil? (Diamond Head)
Lemonheads - Mrs Robinson (Simon & Garfunkel)*
Saga - The Snow Fell (Skrewdriver)
Machine Head - Hole In The Sky (Black Sabbath)*
Gary Jules - Mad World (Tears For Fears)
Eddie Vedder - I Won't Back Down (Tom Petty)*
*Perhaps not better than their originals but still good covers. I hate when artists make a cover that sound exactly like the original, what's the point?
Also worst cover I have ever heard in my life is Scissor Sisters making a cover of Pink Floyd's Comfortably Numb, can't remember the feeling exactly but I know I had a physical pain around my heart hearing it.