Covers that are better than the original
SuBo - I Dreamed A Dream. 
Frankie goes to Hollywood did a superior version of "Born to run" on the PleasureDome LP.
Also it would normally be sacrilege to cover a smiths tune but Dum Dum Girls did a great version of "There is a light which never goes out"
Steps - Tragedy
.
Led Zep with Joan Baez' Babe Im Gonna Leave You
Jeniffer Waarnes with Leonard Cohen's First We take Manhattan.
Hendrix with Dylan's All Along The Watchtower and the U2 version of this as well.
I have both, and enjoy both, but I think the White Stripes cover of Jolene is better:
Dolly Parton: http://www.youtube.com/watch?v=1plvBR02wDs
White Stripes: http://www.youtube.com/watch?v=H4rYaLBUpLA&feature=related
G N R - Live And Let Diiiiieeeeeeee - oooohhhhh yeah!
Sorry gel, but NO NO NO
Marie Queenie Lyons - Fever http://www.youtube.com/watch?v=fHOnM4yDOrc
Patti Drew does a good version, but nothing beats this
Incredible Bongo Band - Apache http://www.youtube.com/watch?v=zjiU2YAlYKY
You'll have heard a mix of this on an advert
Johnny Keating - Jesus Christ Superstar http://www.youtube.com/watch?v=tdATQX6vf1M
Not bad for the guy who did the theme from Z Cars, and just listen to that Moog go
Pat Benatar - Wuthering Heights
G N R - Live And Let Diiiiieeeeeeee - oooohhhhh yeah!
Sorry gel, but NO NO NO
I used to not like it when I first heard it but now I think it's awesome! Axl's voice when he is singing it live is just brilliant!
AND Button Down Brass - Tequila http://www.youtube.com/watch?v=oxmqv3Rc4-M
Best version I've heard
G N R - Live And Let Diiiiieeeeeeee - oooohhhhh yeah!
Sorry gel, but NO NO NO
NO!!!!!!!!
I used to not like it when I first heard it but now I think it's awesome! Axl's voice when he is singing it live is just brilliant!
A case of you - Prince
Rollin' and tumblin' - Jeff Beck
Just one smile - Blood Sweat and Tears
Ruby baby - Donald Fagen
Bobby Fuller Four - Magic Touch http://www.youtube.com/watch?v=4QTDlHzfuDs
One of my all time faves, just brilliant!
Nick Cave - In The Ghetto
Kate Bush - Rocket Man
June Tabor - Don't Think Twice
+ 1 for Jeff Buckley Hallelujah and for his version of Lilac Wine
In the spirit of mutual support I will +1 your In The Ghetto, although also like El Vez's In The Bhario
Shaun