I'll second Annie Lennox's version of Whiter Shade Of Pale. It is a truly rare thing when a cover transcends the original.
Chris Isaak's version of I Want You To Want Me comes very close to transcendence.
For sheer fun I would suggest listening to The Dickies version of Knights In White Satin.
[SIZE=-1]Sarah McLachlan covering XTC's Dear God is always a special treat.
What should be a big ball of kitsch, but actually an amazing thing is Dolly Parton and [/SIZE]Ladysmith Black Mambazo covering Peace Train.
Others that come to mind:
Fine Young Cannibals - Suspicious Minds
Klaus Nomi - Ding Dong! The Witch Is Dead
Klaus Nomi - Lightning Strikes
Radiohead - Video Killed the Radio Star
The Butthole Surfers - Hurdy Gurdy Man
Toad the Wet Sprocket - Hey Bulldog
The Bangles - Hazy Shade of Winter
Bob Marley - Jammin
Peter Tosh - I can See Clearly Now
And in case you didn't know...
http://www.coverville.com/