Like the subject says

G n' R - Knockin' on Heaven's Door (Led Zep)
Stone Temple Pilots - Revolution (Beatles)
Stone Temple Pilots - Dancing Days (Led Zep)
Primus - Devil Went Down to Georgia (Charlie Daniels Band)
Deadsy - Tom Sawyer (Rush)
Nirvana - The Man Who Sold the World (David Bowie)
Aaron Lewis - Black (Pearl Jam)
Cake - I Will Survive

Beatles - Twist & Shout
Machine Head - Negative Creep (nirvana)
cant think of many more, guess i dont buzz off many covers.

Children of Bodom - Silent Scream (Slayer)
Ensiferum - Battery (Metallica)

Travis - Hit Me Baby One More Time
Noel Gallagher - You've Got To Hide Your Love Away
Coldplay - You Only Live Twice

Travis - Hit Me Baby
Cake - I Will Survive
Jeff Buckley - Hallelujah
Oasis - I am the Walrus
Granddaddy - Revolution
Rufus Wainwright - Across the Universe (1,000x better than the original)
Stereophonics - Dont Let Me Down
Gary Jules - Mad World
U2 - Happiness is a Warm Gun
The Vines - I'm Only Sleeping

How the hell did I forget those?

You were busy thinking about how hot it would be to see Liam and Noel go at it.... ?

Anything on Iced Earth - Tribute to the Gods.

I dunno about 'hot', but that would sound foo*ing hilarious.

Nirvana's "Molly's Lips" and "Son of a Gun" which are covers of The Vaselines' songs, and also Nirvana's "Where Did You Sleep Last Night?", a cover of a Leadbelly song. I also really like Orgy's "Blue Monday", a cover of the New Order song.

Cradle of Filth - Hallowed be thy Name
Sonata Arctica - I Want Out, Fade to Black
Monte Montgomery - Sultans of Swing
Me - Master of Puppets

Det - I know you like Dire Straits, you should really check that cover out if you haven't already.

Oasis - Hello
Oasis - MY Generation

Bands shouldn't cover songs by bands that are better than they are.

Examples of this are:

Korn - Another Brick In the Wall
Blink182 - Lovesong
Linkin Park - Wish


Incase you're braindead, no covering The Floyd, the Cure, or the NIN... in the end you're just butchering a good song.

I'm going to add The Who to that list too...

(Granted I've hear some wicked who cover's from older bands, but like I said don't cover songs by bands that are better than you are... most of the older ones are on the same tier in my opinion...)

Pearl Jam - Rockin' in the Freeworld
Pearl Jam - Leavin' Here
Neil Young - All Along the Watchtower

Snake River Conspiracy - Lovesong (The Cure cover)
No Doubt - It's My Life (Talk Talk cover)

Gary Jules - Mad World is a cover? Add that to the list then.

Cake - I Will Survive
Bandits of the Acoustic Revolution - Dear Sergio

Plenty of others, just can't think of them atm.

Grey Matter - I am the Walrus (beatles)
Stevie Ray Vaughn - Voodoo Child (Jimi Hendrix)
Tea Party - Paint it Black (Rolling Stones)

I'm pretty sure Dylan wrote that

Anywho,
Nirvana-Man Who Sold The World ( Bowie )
The Doors - Gloria (Van Morrison)
Johnny Cash - Hurt (NIN)
Hendrix - All Along The Watchtower ( Bob Dylan)

My mistake. Thought this was a thread about album art.

Marilyn Manson - Sweet Dreams (Eurhythmics)
Marilyn Manson - Personal Jesus (Depeche Mode)
System of a Down - Snowblind (Black Sabbath)
Brent Spiner - Sway (?)
Disturbed - Shout 2000 (Tears for Fears)
Gary Jules - Mad World (Tears for Fears)
KoRn - Low Rider (War)
Nirvana - The Man Who Sold the World (David Bowie)

Tomoyasu Hotei - Immigrant Song (Led Zeppelin...duh)

Alien Ant Farm- Smooth Criminal (M.J.)

I love that song

Forgot another one..

Muse - Cant Take My Eyes Off You

Five Iron Frenzy - It's Not Unusual (Cher, I think )
Fanmail - I Want It That Way (The Backstreet Boys)

Jesus Don't Want Me For A Sunbeam is also sort of a Vaselines cover.
I used to like Orgy's version of Blue Monday. I heard it just when I was starting to get into New Order. Then I started to really like the original and realized that Orgy's version really kind of sucks. They change the whole thing into this angsty crap, and it's missing the awesome drums and coldness of the original.

Nirvana- Man Who Sold the World (David Bowie)
Nirvana- Love Buzz (Shocking Blue)
Nirvana- Plateau, Oh Me, and Lake of Fire (The Meat Puppets)
Nirvana- Here She Comes Now (The Velvet Underground)
Nirvana- Where Did You Sleep Last Night (Leadbelly)

The Beatles- Twist and Shout (Isley Brothers)

Toad the Wet Sprocket- Hey Bulldog (The Beatles)

Urge Overkill- Girl You'll Be A Woman Soon (Neil Diamond)

The Pretenders- Something to Believe in (The Ramones)

Lapdog- Father Christmas (The Kinks)

The Pixies- Head On (The Jesus and Mary Chain)
The Pixies- Hang On To Your Ego (The Beach Boys)
The Pixies- Winterlong (Neil Young)

REM- The Passenger (Iggy Pop)

Bauhaus- Ziggy Stardust (David Bowie)

Echo and the Bunnymen- People Are Strange (The Doors)
Echo and the Bunnymen- All You Need is Love (The Beatles)

Pavement- The Killing Moon (Echo and the Bunnymen)

Box Tops- Whiter Shade of Pale
Box Tops- You Keep Me Hanging On

AFI- The Hanging Garden (The Cure)

Yo La Tengo- Little Honda (The Beach Boys)

Nope, it's Tom Jones.
I really like their cover of ELO's Sweet Talkin' Woman.

Johnny Cash- Hurt (NIN)
Uncle Tupelo- No Depression (Carter Family)

Pearl Jam - Rockin' in the Freeworld
Stevie Ray Vaughn - Little Wing
Stevie Ray Vaughn - Voodoo Child
Jimi Hendrix - All Along The Watchtower

Now that's my favorite cover.

The Burning Paris - Asleep (The Smiths)
Bodyjar - Racist Friend (They Might Be Giants)
Suicide Machines - End Of The World (REM)

I love that song, but I'm not sure if it counts or not. I think Jimi Hendrix recorded it before Bob Dylan.

It's kind of like Leonard Cohen's song Suzanne. A friend of his recorded it and it became a hit, and then he went into music and recorded his own version. I don't know if doing someone else's song before they record it is a cover or not.