I was going to post that! More proof that Richard Thompson is a higher being than the rest of us.
I saw him do it live at the Bumbershoot music festival in Seattle in 2002. Nobody in the crowd knew what was coming. It was outstanding.
YES! Finally someone else says what I have been saying for years. I hate that goddamn song (Hallelujah). What a bunch of boring, melodramatic, emo drivel. Ugh! I hate the lyrics so much. I especially hate Rufus Wainwright’s version.
Joss Stone’s cover of “Fell In Love With a Girl” (changed to “Boy”) is every bit as good as the original by White Stripes.
Johnny Cash, Hurt.
melt I love you.
Here’s a web site with info and tons of streaming music. Thank you!
Disclaimer: I swear on a stack of Happy Rhodes albums that I did not pay happycamper*5 a dime to post.
I love Leonard Cohen, but people needed to stop covering “Hallelujah” years ago. Especially since most of them are just covers of the 1994 Jeff Buckley cover. It’s been done, a’right?
Guitar Wolf’s cover of “(I Can’t Get No) Satisfaction”
Nashville Pussy, “First I Look At the Purse”
Two good ways covers should be done.
Covers that not only are great but totally reinterpret the song:
Stand By Your Man, Candi Station
Heartbreak Hotel, John Cale (of Velvet Underground fame)
And a cover so atrocious it’s hilarious, the Brady Bunch cover “American Pie”. You were warned.
I’m surprised this hasn’t had a mention yet.
Jeff Buckley’s version was based on the 1991 one by John Cale. I agree that the song’s been over-covered, but Cale’s cover is a slice of awesome, and that’s the standard I aspire to in my performances of it … in my shower.
Is that a full-sized guitar?
Dude…that’s a ukulele. 
ETA: In your face covers don’t get much more…in your face than Social D’s cover of Ring of Fire…
Good - Seether’s version of George Michael’s “Careless Whisper”
Bad - Sarah Brightman’s version of Queen’s "Who Wants To Live Forever.
Ugly - Sebastian Bach’s and Axl Rose’s cover of Aerosmith’s “Back in the Saddle.”
The good - Guns and Roses - Since I Don’t Have You. Surprisingly good.
The bad - Eddie Vedder - Love Reign O’er Me. Just lame.
I agree that the lyrics suck*, but I love the way the song sounds. And I think Justin did a sufficiently different version than the ones I’ve heard before.
*Okay, I like the part about the chords, as he’s playing the exact chords he’s singing about. And I do think the lyrical history is interesting.
Yannick’s Ce Soiree La, a French rap cover of the Four Season’s Oh What A Night, ended up being added to the Broadway musical Jersey Boys.
You might find some examples in this thread:
Covers of Songs That Radically – And Successfully – Re-interpreted the Work
It’s one of my favorites on the dope.
I heard on the radio, back when her cover was current, that Ms. Hill had apparently never heard of Janis Joplin when she recorded the cover. That surprised me; she’s only about a year younger than me and I heard of JJ way back when I was a teenager.
Let’s see, how about Aidan Powell’s wonderful rendition of Train’s “Hey Soul Sister”?
This viral video of Robyn’s Call Your Girlfriend by 3 members of some group called Erato blows me away. Not just the cup gaming - I think it’s a legitimate, and much better, version of the song.