Covers that are better than the original

This could be controversial I know, but sometimes - just sometimes - someone does a cover of a song and raises it above whatever previous heights it had achieved. More often than not though, a really good cover is a song that wasn't very famous in it's original incarnation.

So, here goes...

Cyndi Lauper's version of Prince's 'When you were mine':

The Kill's version of The Velvet Underground's 'Pale blue eyes':

Jimi Hendrix's era defining version of Bob Dylan's (quite frankly boring) 'All along the watch-tower'. So seminal, that Dylan started playing Hendrix's version at concerts:

The White Stripes - 'I just don't know what to do with myself', first performed by Dusty Springfield:

Angus and Julia Stone's quiet version of 'You're the one that I want', sung by Olivia Newton John in Grease.

I REALLY want to put the McGarrigle's version of Loudon Wainwright's 'The Swimming Song' in this list but it's nowhere to be found.