The Top Notes’ “Twist and Shout” as covered by the Beatles
Ritchie Cordell’s “I Think We’re Alone Now” as covered by Tiffany
Joan Baez’s “Diamonds and Rust” covered by Judas Priest
I have to say I like Metallica’s version of “Whiskey in the Jar” over The Dubliner’s version. I also like They Might Be Giant’s version of Istanbul (Not Constantinople) over The Four Lads version. Oh and Pearl Jam doing Last Kiss the right way, all mournful and sad, not peppy and dance-to-itiveness like J. Frank Wilson And The Cavaliers. Way to be cavalier about killing your girlfriend in a car wreck!
Tom Paxron admits he likes the Fireballs’s hard rocking version of his “Bottle of Wine” better than his own golk verson.
Timeless (Korean cover) - by Zhang Liyin and Xiah Junsu
Timeless (English) - by Kelly Clarkson and Justin Guarini
If we’re including foreign language covers, you have not heard the best version of New York New York until you hear Dudu Fisher’s Hebrew version.
Jeffrey Gaines’ version of Peter Gabriel’s In Your Eyes.
http://www.youtube.com/watch?v=o7WtavVdBCk&feature=related
I love the original, but the acoustic version is amazing.
Thank you! Enjoying it right now.
Lots of good ones I agree with upthread. I’ve been raving about K.D. Lang’s version of Hallelujah long before she did it for the olympics. I have to chime in with the people on Johhny Cash’s version of hurt, which I like a lot more, even though in general I prefer NIN to Cash’s music. Though Cash did do an awesome version of God’s Gonna Cut You Down
The one I didn’t see that simply blew me away was Tori Amos’ cover of Smells Like Teen Spirit by Nirvana. Of couse, I also preferred Wierd Al’s parody so maybe I’m a bit biased. 
She also did a wicked cover of Famous Blue Raincoat that was originally done by Leonard Cohen. As much as I think Cohen was a genius of a writer, as a performer … I’ve heard a lot of covers of his stuff that I like better.
And someone mentioned Eva Cassidy upthread, she did a cover of Time After Time that I loved. Also, Sarah McLachlan’s version of Dear God was better IMO than the original by XTC And Sarahs’ cover of Joni Mitchell’s River is my favorite Christmas song of all time.
This song just seems to work as a solo acoustic thing. I was once in a coffee shop while a young woman was playing a guitar. I don’t think it was either an official “open mike,” nor a scheduled performance. There was no evidence of either. It seemed more like she was just a friend of somebody, had her guitar, and somebody suggested she play a few tunes. There were several people in the shop and nobody was visibly paying her any attention at all. Truth be told, she wasn’t particularly great in the first few tunes while I was there.
Then she played this song. I recognized it at the first notes, and between that moment and the end of the first lyric, the place hushed, and everybody listened. It wasn’t perfect, but somehow it was very affecting. Everybody applauded, and she blushed. 
Except for California Girls.
Rogers & Easton We’ve Got Tonight > Cocker
Metalheads on here might hate me, but The Cardigans cover of “Iron Man” was really cool. It was a completely different feel from Black Sabbath, but it’s got this cool, breezy feel to it. I prefer it.
I prefer Joan Osborne’s version of What Becomes Of The Brokenhearted to the original.Jimmy Ruffin’s version always sounds so flat.
[heresy] David Ruffin’s version of I Want You Back is better than the original [/heresy]
Jimi Hendrix’s version of Wild Thing. It’s even more successful than All Along the Watchtower in that I think people forget it’s a cover. The Troggs’ version (not the original, as it turns out) has an ocarina solo. How were they supposed to compete with Jimi Hendrix?