Just a dissenting opinion–I find that the weakest track on an otherwise fantastic album (Broken English). I don’t think anyone can really pull off a cover of that song (though I guess she comes closer than anyone else). The original is just too nakedly personal. It belongs 100% to Lennon.
Celine is the musical opposite of bacon salt: anything you add her to becomes unpalatable.
Just got my Eva Cassidy CDs. God, how beautiful. (Fields of Gold currently playing.)
Davied Byrne ending a concert with Whitney Houston’s “I Wanna Dance with Somebody.” Well done, Mr. Byrne!
Seconded, big time!
I am a Tom Jones fan, and have been since childhood. This is one of very few covers that I actually prefer to the original.
It was actually a regular song in his live shows before he finally recorded it.
My vote goes to Alanis Morrisette 's cover of “My Humps”, though more for the video than the song itself.
For me, that would be Elton’s Lucy in the Sky. Yeah, I know. Heresy. But still.
There were nothing but covers on that album. It was basically a recorded warm-up session for Zevon’s Sentimental Hygiene (1987), on which the threee REMmers played a bit (in addition to Zevon’s usual suspects.)
Ooh! Tom Jones doing Procol Harum’s “Simple Sister” on a tribute album. I almost put the CD back in the rack when I saw his name. Wrong! He rocks like hell on that song! BTW, I recently Netflixed the first disc of the This Is Tom Jones DVD, mainly to see the Moody Blues and the Who, but the man was pretty awesome himself.
I would have to agree with you, Lib. Although, for me that’s probably because I heard Elton’s version first.
Wow. How did that happen? The Beatles had been fairly ubiquitous. (Not doubting you, just genuinely curious.)
Oh yeah, I know. I still have the cassette. 
But the OP was about covers that surprised you, and it was definitely Raspberry Beret that really got me to sit up and take notice. As I recall, it even got radio attention.
Another striking cover is Alien Ant Farm’s cover of Michael Jackson’s “Smooth Criminal.” I heard it and was blown away. I’d almost forgotten the song, actually like the cover better. Some younger people don’t even know that MJ wrote the song.
I generally dislike No Doubt, but I kinda like the cover of Its My Life.
Off topic: I truly wish I could have this appreciation for Eva Cassidy that everyone else seems to have. I have friends who would choose her stuff as their only music on a desert island, yet her stuff does nothing for me. It’s so weird, because I love covers and she seemed to love them too. I just found (nobody shoot me, okay?) that her interpretations seemed so hollow and a little too “listen to my hypnotizing voice” for me.
Then again, I only listened to a few after not liking those. Can you suggest some of your favorite songs of hers? I still have all of her CDs so I can easily listen.
Ryan Adams’ version of Alice in Chain’s “Down in a Hole” is amazing. I almost like it more than the original.
Sleeps with Butterflies writes:
> Can you suggest some of your favorite songs of hers?
“Somewhere over the Rainbow.”
Jimmy Buffett’s cover of Southern Cross. I mean, it’s just so Buffett. Moreso than Neil Young, IMO.
Tori Amos covering Slayer’s “Raining Blood” was pretty weird.
Also, Motorhead’s cover of “Stand By Your Man.”
I wouldn’t sweat it, Sleeps. Nobody is going to have 100% universal admiration. For me with her, it is much less about the songs themselves and much more about her voice. And that’s a very subjective call.
I also discovered Coverville through my Tivo. I get it in iTunes now.
I’m a big fan of covers, especially unusual ones. Such as folky covers of rap songs:
“Bring the Noise” by Brent Runyon
“Baby Got Back” by Jonathon Coulton
and especially “Straight Out of Compton” by Nina Gordon
Nouvelle Vague are like Me First and the Gimme Gimmes in reverse. They convert songs from Punk (and New Wave), into Bossa Nova. Of the songs I’ve heard, my favorite is “Love Will Tear Us Apart”, but the most surprising would be “Too Drunk to Fuck”.
Speaking of “Love Will Tear Us Apart”, there’s a cool dub version by a group called Jah Division.
The Clash’s “Hateful” by Stevie Mac is nice.
Living Colour covered Tracy Chapman’s “Talkin’ 'Bout a Revolution”.
The T.A.T.U. version of “How Soon is Now?” is a guilty pleasure.
Funny you should mention that particular cover.