Pearl Jam does a great cover of Dylan’s Masters of War
Beatles “Twist And Shout”
Annie Lennox - a lush version of ‘Whiter Shade of Pale’
Eva Cassidy - ‘Somewhere Over the Rainbow’
Bonnie Raitt - ‘Runaway’ (RIP Norton Buffalo)
Sinead Lohan’s cover of Dylan’s To Ramona is fantastic.
I also like Stevie Nicks’ version of Free Fallin’.
Lots of good ones if you scrounge around YouTube for a while.
This probably won’t go over well, seeing as I’m also a fan of Orgy’s take on Blue Monday, but I love the Ataris’ version of Boys of Summer.
I see nobody has mentioned Goldfinger’s version of 99 Red Balloons yet. Pure awesomeness.
Niyaz’s version of the Cure’s Lovesong.
I have that in my collection. It is indeed awesome. By an extraordinary coincidence (or perhaps not, Ensign Ricky?), it is on the soundtrack to Not Another Teen Movie, which also includes the much-maligned Orgy cover of Blue Monday being so bandied about elsewhere in this thread.
Along those same lines (covers of songs by one-hit wonders that have dropped off the face of the Earth - or at least gone back to Germany), I can’t believe I forgot to mention Save Ferris’s cover of Come On Eileen by Dexy’s Midnight Runners. I guess I scrolled right past it while going through my playlist.
Ted Leo (of Ted Leo and the Pharmacists) does a great tongue-in-cheek cover of Kelly Clarkson’s Since U Been Gone
Milow’s Ayo Technology, originally done by 50 Cent and Justin Timberlake.
I was a little metalhead when I was younger and Metallica’s Stone Cold Crazy will always have a special place in my heart over Queen’s version.
The White Stripes cranked the insanity to 11 with I just don’t know what to do with myself, a take Dusty Springfield would have approved of.
James Taylor was a singer-songwriter, but most of his hits were cover songs.
I love Holly Cole’s I Can See Clearly Now
Gotye’s Somebody That I Used To Know, with Kimbra, is great. But Walk Off The Earth’s cover of it is pretty damn good, especially the five people playing one guitar trick.
Somebody actually made a video of the two versions (Gotye’s music video version) side by side - this was really neat.
That is freaking brilliant! Thanks. 
It’s staged. We had a dedicated thread on that song last week, and they admit they’re not live in that vid..
Here’s another Comfortably Numb cover - bluegrass style!
Luthor Wright and the Wrongs - Comfortably Numb
Good question, and I think the votes would be divided on it.
The above are Taylor’s hits. He wrpte the first two, but the other three are ciovers.
Mockingbird is the most unusal, and best, cover to hit the top 5.
I’m sure I’ve posted this in one of these threads before, although Oasis wrote this song, Ryan Adams owns it:
I’ll add The Civil Wars doing Leonard Cohen’s Dance me to the end of love.