So, here's a sample from my "great cover versions" playlist on the ipod... I wouldn't say that all of these are necessarily better than the originals, just different, but I have marked with an asterix a few that I think of as being the best version so far.
Peace Train - 10,000 Maniacs
I scare myself - Thomas Dolby
Song to the Siren - This Mortal Coil
Black Magic EWoman - Santana
Giving it all away - Roger Daltry*
Thin Line Between Love and Hate - Pretenders
The First Cut is the Deepest - Martin Simpson
Wonderful World - Otis Redding
Another Saturday Night - Cat Stevens
This Flight Tonight - Nazareth
From a Distance - Nanci Griffith (covering Julie Gold, not Bet Midler!)*
Song from Under the Floorboards - My Friend The Chocolate Cake
Can't Stand the Rain - Lowell George
Glory Box - John Martyn*
Oh Well - Joe Jackson
Bird on a wire - Jennifer Warnes*
Hallelujah - Jeff Buckley*
One Love - Jason Mraz
Summer Breeze - Isley Brothers*
Love the one you're with - Isley Brothers
Walk on by - Isaac Hayes
Suspicious Minds - Fine Young Cannibals
Cocaine - Eric Clapton
Say hello, wave goodbye - David Gray
I will survive - Cake
Guitar man - Cake*
Twist and Shout - The Beatles*
Blinded by the light - Manfred Mann's Earthband