The two big, well-known ones that always come to mind for me are:
- Devo's cover of the Rolling Stones' "Satisfaction"
- Cowboy Junkies' cover of the Velvet Underground's "Sweet Jane"
But all these are also great:
- Alien Sex Fiend's cover of the Cramps' "Silver Machine"
- Cornelius's cover of the old, old song "Brazil" (according to Wikipedia written by someone named Ary Barroso)
- Faith No More's cover of the Dead Kennedys "Let's Lynch the Landlord"
- The super-sleezy Motorhead/Wendy O. Williams cover of Tammy Wynette's "Stand By Your Man"
- Mike Ness' cover of Bob Dylan's "Don't Think Twice"
- REM's cover of the Velvet Underground's "Pale Blue Eyes"
- Also REM's cover of the Clique's "I Am Superman"