Jimi Hendrix Experience - All Along the Watchtower (Bob Dylan):
Santana - Black Magic Woman/Gypsy Queen (Fleetwood Mac/Gábor Szabó):
The Byrds - My Back Pages (Bob Dylan):
Manfred Mann's Earth Band - Blinded by the Light (Bruce Springsteen):
Johnny Cash - Hurt (Nine Inch Nails):
Stevie Ray Vaughan - Little Wing (Jimi Hendrix):
Dead Kennedys - I Fought the Law (The Crickets, albeit with a few liberties taken to the lyrics):
Metallica - Am I Evil? (Diamond Head):
Emperor - A Fine Day to Die (Bathory):
I could go on. I apologise in advance if I have already taken all of someone's favourites.
Terrible covers include Madonna's ruination of Don McLean's "American Pie" and Britney Spears' desecration of the Rolling Stones' "Satisfaction" (actual good covers have been recorded by Devo and the Residents, although neither is recognisable as the same song and the latter in particular will probably sound like noise to a lot of people here).