In an absolutely horrible segue, Ray Charles (both cool & blind) - Georgia On My Mind by Hoagy Carmichael and Stuart Gorrell.
Stone Cold Crazy -Metallica by Queen
The Indigo Girls did a 2-CD cover of the entire recording of Jesus Christ Superstar.
Credence Clearwater Revival (CCR) - “I Put a Spell on You” by Screamin Jay Hawkins
Aretha Franklin - “Respect” by Otis Redding.
I think we are losing track of the “singer-songwriter” part of the OP and are just listing all covers now.
Not to mention Feist - “1, 2, 3, 4” by New Buffalo (aka Sally Seltmann).
Never mind. Misread OP.
Huh-wut? 
Really? I’ve never heard of this. Conceptually, it makes my head a little explodey.
We need a head explodey smiley.
I think that was already lost in the OP. (Manfred Mann’s Earth Band?)
Whoa, you are serous about this, aren’t you? Had no idea The Carpenters ever covered that song.
And the 30 second clip here http://www.last.fm/music/Carpenters/Gold%3A+Greatest+Hits didn’t sound bad at all.
Here’s the whole wonderful thing, lip synced on some show, with a very silly intro, but it’s worth it once the song kicks in. Middle America didn’t know what to make of it. It was way ahead of its time.
Edit to add, here’s the Klaatu version, for those who haven’t heard it.
Oh, never mind that one, here’s a Star Trek-related fan video that’s very cool, very well done. I just found it.
Edit to add, here’s a fairly decent re-mix.
Oh god, now I’m on a Carpenters kick. Love 'em!
And then the response after that : The Pointer Sisters.
Bonnie Raitt covered Angel From Montgomery by John Prine.
Steve Goodman covered a whole bunch of Prine’s songs, and vice versa.
Johnny Cash, Kris Kristofferson and Willie Nelson all covered each other’s music extensively.
Warren Zevon covered Prince’s Raspberry Beret
Bob Dylan covered Zevon’s “Mutineer”
Bruce Springsteen covered Zevon’s “My Ride’s Here”
Jackson Browne and Linda Ronstadt both covered Zevon’s “Poor Poor Pitiful Me”
Steve Earle covered Zevon’s “Reconsider Me”
Don Henley covered Zevon’s “Searching for a Heart”
Cheap Trick covered Big Star’s “In the Street” (“That 70’s Show”)
Harry Nilsson–“Everybody’s Talkin’” by Fred Neil, and “Without You” by Pete Ham and Tom Evans.
Steve Miller Band - “Jet Airliner” by Paul Pena
Foghat - “I Just Want to Make Love to You” by Willie Dixon
Arlo Guthrie made a hit out of Steve Goodman’s City of New Orleans.