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Which studio recorded (ie non concert) ones do you like?
It is rare that a cover version is as good as, let alone better than the original. The most successful ones tend to be a differnt take on the original rather than a note for note copy.

Jimi Hendrix - All along the watchtower (in fact most of Jimi's covers are pretty good)
Joe Cocker - A little help from my friends in a different league to the Sgt Pepper original
Sinead O'Connor - Nothing compares to you Prince who?

But personally, the one I most enjoy is the FNM treatment of War Pigs; it follows the Sabbath version but has a bit more snap to it, the drums sound superb (Mike Bordin now plays in Ozzy's band, so he must have made an impression)

not really a vid, just the track, crank it up and enjoy.

Jeff Buckley - Lilac Wine and Halleluja. Two of the best covers one one album.

The Australian Pink Floyd Show - all of it, but especially the 'Animals' pops CD.
'You Really Got Me' - Van Halen.
'Delilah' - The Sensational Alex Harvey Band.

Slightly off-topic, but I give a lift to a young work colleague occasionally and one day recently Comfortably Numb was on the CD, and he said, quite seriously, "It's not as good as the original by the Scissor Sisters"!!    Kid's today eh?  : I nearly stopped the car and asked him to get out. 

Rush - The Seeker

One of my favourite covers.

some good suggestions 

I should have said I was interested in studio versions rather than concert recordings.  Many bands have covered songs when playing live.