I think Less Than Jake did a fine job on their Ska covers of the Grease soundtrack.
Kiss- Prince
Kiss -Art of Noise with Tom Jones
I recently picked up a copy of something called “A Metal Tribute to ABBA”, and though I’ve never heard of a single band on it, someone called Rough Silk does a kickass job with Take A Chance On Me. That “takeachance-takeachance-takeachchchancechane” line from the original is turned into a killer metal riff.
I also seem to like Bob Dylan’s stuff better when it’s performed by other people. All Along The Watchtower by Hendrix, Wanted Man by Johnny Cash etc.
Prince-I feel for you
Chaka Khan - I feel for you
The Family - Nothing Compares 2 U
Sinead O’Connor - Nothing compares 2 U
Summer Wind - Isley Bros
Fire and Rain - Isley Bros, I love both of these much more than the originals.
Tears of a Clown - English Beat
Johnny B. Goode - Peter Tosh
Mi Manera (My Way) - Gipsy Kings
Smashing Pumpkins’s cover of “Landslide” is amazing.
I’m also a fan of anything **Barenaked Ladies ** covers - “Material Girl,” “Fight the Power,” and “Careless Whisper” are my favorites…
Tori Amos had a great album of covers a few years ago called “Strange Little Girls.” Her cover of Emenem’s “87 Bonnie & Clyde” is haunting.
Ooh, covers. It’s fun to see what a different artist can do with a song. Sometimes it can turn a song you previously hated into something you really like. For example, I hate “Careless Whisper” but I like the cover version with Ben Folds and Rufus Wainwright. It is just so melodramatic, it’s great.
Other covers I like:
Wonderwall - Ryan Adams (Oasis)
Bitches Ain’t Shit - Ben Folds (Dr. Dre). This is easily the most profanity laden song on my computer, quite a contrast with the pretty piano melody.
Since U Been Gone - Ted Leo (Kelly Clarkson). He added the chorus of “Maps” by the Yeah Yeah Yeahs near the end. Strange but it works.
Girls Just Wanna Have Fun - Ben Gibbard (that guy from Death Cab for Cutie)
Scissor Sisters take on Comforatbly Numb.
First two songs that come to mind:
I Heard it Through the Grapevine- CCR
Across the Universe - Fiona Apple
Sonic Youth’s version of Computer Age by Neil Young is the better of the two (by a large margin).
The Disposable Heroes of Hiphopracy’s version of California Uber Alles by the Dead Kennedys is very different from, but just as good as, the original.
I like Sonic Youth’s version of Superstar, made famous by the Carpenters, written by Leon Russell, I believe.
Also Cowby Junkies’ cover of Sweet Jane.
mariemarie, also on that Carpenters disc is Sheryl Crow making Solitaire her own.
And on the Honeymoon in Vegas soundtrack is the version of Love Me Tender that the song was waiting forever for Amy Grant to show up and record.
I see a Ben Fold’s cover upstream, and I raise ya’ Ben Kweller’s Bk Baby. It isn’t just a funny “look at the white boy go” cover, it’s actually pretty great to rock out to.
In a similar vein, Goldfinger’s “99 Red Balloons” is hella fun for dancing around and breaking stuff. Likewise, NOFX’s “Vincent” is a fun punk pop number. I resisted liking it for years, since I thought it was smelling up McLean, until I realized I could like both at once.
Camper Van Beethoven’s “Interstellar Overdrive” is amazing, while They Might Be Giant’s “How the Sun Shines” is both amazing and amazing.
If you consider them covers, then Pete Seeger’s “Casey Jones” and “Big Rock Candy Mountain” are both classics.
Led Zeppelin did just enough different with “When the Levee Breaks” to warrant a cover, but they did everything just right.
As a couple of others said, I could go on forever. I listen to music way beyond the point of a healthy obsession, almost to the point where several chord progressions and an entire community of augmented quarter notes have tried to get me placed behind bars.
"I’m a Believer" - I prefer bee-bopping to the Monkees version over Neil Diamond’s
“Red, Red Wine” - I also prefer UB40’s version over Diamond’s. (Hey, I appreciate his song writing at least)
“Here Comes the Sun” - Believe it or not, but I like Sandy Farina’s (from the notorious “Sgt. Peppers” movie) to the Beatles
“Something (in the way she moves)” - Speaking of the Beatles, I like Elvis’ version to the Beatles. His gospel influence works well with this song
"The Beautiful Ones" - I prefer Mariah Carey and Dru Hill’s duet to Prince’s version from “Purple Rain.” Though, honestly, the best version is not even available to purchase AFAIK. The live version from the movie kicks ass. I wish an audio file of it was available.
“I Walk the Line” - The man in black has been trumped by an American Idol contender, Chris Doughtry, who apparently copped it off Live. (I’ve heard Live’s version; I prefer Doughtry.)
“Somewhere Over the Rainbow” and “Fields of Gold” - Eva Cassidy gives a jazzy interpretation to these great songs
“I Want to Know what Love Is” - Australian songstress Tina Arena knocks this one out of the ballpark. Foreigner’s pales in comparison. Check out the video here .
I’m addicted to cover songs, especially ones that cross genres. A few of my favorites, just off the top of my head:
Alien Ant Farm - “Smooth Criminal” (Michael Jackson)
Anthrax - “Got the Time” (Joe Jackson)
Bauhaus - “Ziggy Stardust” (David Bowie)
Exodus - “Low Rider” (War)
Fear Factory - “Cars” (Gary Numan)
Goldfinger - “Rio” (Duran Duran)
In Flames - “Everything Counts” (Depeche Mode)
Insane Clown Posse - “Let’s Go All The Way” (Sly Fox)
Johnny Cash - “Rusty Cage” (Soundgarden)
Nevermore - “The Sound of Silence” (Simon & Garfunkel)
Nightwish - “Over The Hills And Far Away” (Gary Moore)
Orgy - “Blue Monday” (New Order)
Pseudo Echo - “Funky Town” (Lipps, Inc.)
Sepultura - “Orgasmatron” (Motorhead)
Smashing Pumpkins - “Clones (We’re All)” (Alice Cooper)
Van Halen - “Pretty Woman” (Roy Orbison)
Voi Vod - “Astronomy Domine” (Pink Floyd)
I’m pretty sure you have that wrong, for two reasons:
- I remember reading stuff about why she wrote it
- There’s no way anyone else could have written that song.
Patti Smith- “When Doves Cry” (Prince)
The Pixies- “Winterlong” (Neil Young)
The Pixies- “Head On” (Jesus and Mary Chain)- I liked this one so much that the original one disappointed me at first.
David Bowie- “Across the Universe” (The Beatles)- It’s funny how he doesn’t sing the “jai guru deva” part. My guess is because he couldn’t figure out what those words were.
David Bowie- “God Only Knows”
Big Star- “Femme Fatale” (Velvet Underground)- The best VU cover. I’m one of the rare people who likes the original version of Sweet Jane better than the Cowboy Junkies version (though theirs isn’t bad).
Uncle Tupelo- “No Depression” (The Carter Family)- I want to hear the original. It’s a great song.
Soft Cell- “Tained Love” (Gloria Jones)- I didn’t even know this was a cover until recently. When I heard the original, I assumed that that was the cover.
The Replacements- “Black Diamond” (Kiss)- I haven’t heard the original and don’t really like Kiss, but I like this song.
Echo and the Bunnymen- “All You Need is Love” (The Beatles)
David Bowie- “Pablo Picasso” (Modern Lovers)- It’s a lot different from the original, so some will think it’s inferior. It’s much more melodic.
Box Tops- “You Keep Me Hanging On” (The Supremes)- At least I think it was originally by the Supremes. It’s my favorite version of the song, but it’s hard to find.
I’m not sure which version of “Chinese Rocks” is my favorite, they’re all really good.
Save It for Later - Harvey Danger 
I don’t know if this exactly qualifies as a cover, but:
Heard It Through the Grapevine - Gladys Knight and the Pips
It’s the version I remember from my teenage years, but I haven’t heard it played in decades. Unfortunately.
A passel of Dylan covers:
All Along the Watchtower - Jimi Hendrix
If Not for You - George Harrison
Mr. Tambourine Man - Byrds
Chimes of Freedom - Byrds
All I Really Want to Do - Byrds
Two votes for that remark!
“Got to Get You into My Life” by EWF (Beatles)
“Shadows in the Rain” by Sting (Police) (yeah, he redid his own song much better)
“Woodstock” by CSN (Joni Mitchell)
“Every Little Thing” by Ra (Police)
“Superstition” by Jeff Beck (Stevie Wonder)
“America” by The Nice (West Side Story soundtrack)
Many more, I’m sure, that will come to mind later.
Some more I thought of - I tried to make sure none of these were listed above, but my eyes crossed a bit…
Higher Ground - Red Hot Chili Peppers (Stevie Wonder)
Gold Dust Woman - Hole (Fleetwood Mac)
Lovecats - Tricky (The Cure)
Fly - Moxy Fruvous (Tom Waits)
Nothing but Flowers- Guster (Talking Heads)
You Oughta Know - The Dan Band (Alanis Morrissette)
Patti Smith definitely covered Van Morrison’s “Gloria”, but she of course did it in a way only should could: spoken verse seamed perfectly into a great little rock number.
While I’m at it, “My Generation”, the live version off of Horses, is freaking incredible as a song to speed to. I’ll second that recommendation.