Johnny Cash - Highway Patrolmen (orig. Bruce Springsteen)
Cake - I Will Survive
Foo Fighters - Baker Street
Fountains of Wayne - Hit Me Baby One More Time (I like it better than Travis' version)

Cake - I Will Survive
Nirvana - Man Who Sold The World

bob dylan - house of the rising sun
eric clapton - while my guitar gently weeps

Six Feet Under - In league with satan

Ministry - Lay Lady Lay
Ministry - Smothered Hope
Skinny Puppy - Tainted Love
Faith No More - Easy
Dillinger Escape Plan & Mike Patton - Come To Daddy
Sepultura - Procreation (of the wicked)
Frank Zappa - Purple Haze, Stairway To Heaven, Sunshine Of Your Love
Faith No More - Glorybox
1000 Homo Dj's - Supernaut
White Zombie - Children Of The Grave

Rage Against the Machine's Renegade CD has some pretty cool covers in it. I also like Soundgarden's cover of "Come Together". Soundgarden also did a Spinal Tap cover of the song "Big Bottom", which is pretty cool too.

fu manchu - godzilla

I love Johnny Cash's version of Hurt.

Metallica's Whiskey in a Jar and Turn the Page are also great.

String Cheese Incident-Gin and Juice
The Coolies- I am a Rock

Its incredible.

Lou Reed's version of This Magic Moment.

The Black Crowes - Hard To Handle

The Animals - Boom, Boom, Boom, Boom.

New Found Glory had an EP a few years ago with fun covers of The Neverending Story theme song, 'The Goonies r good enough', "The Glory of Love" (from one of the karate kid movies) and a few others.
Johnny Cash has been doing a bunch too, everyone mentions 'Hurt', I like his covers of Soundgarden's "Rusty Cage" and Beck's "Rowboat" too. The Ramones did a killer version of "Street Fighting Man" and Pearl Jam does a great "Sittin' on the Dock of the Bay"

I'll give you three:

Ben Harper - Strawberry Fields (Beatles)
Dave Matthews - All Along the Watchtower (Bob Dylan)
Metallica - Tuesday's Gone (Lynyrd Skynyrd)

Orgy - Blue Monday

Jeff Beck's version of "Goodbye Porkpie Hat" by Mingus.

Anything by William Shatner

Limp Bizkit - Sanatarium (Metallica)
Phish - Gin and Juice (Snoop Dogg)
Marilyn Manson - Sweet Dreams (Eurythmics?)
NOFX - Straight Edge (Minor Threat)
Pearl Jam - Last Kiss (Dunno)
Rancid - Vanilla Sex (NOFX) (Rancid sucks ass though)

There is something about a cover song that hits you in a special way. Maybe it is because you have already been hit with that song and it builds up memories and then bam, you get hit with it again but in a different way... Yeah... Something like that...

Cover song of the moment that hits me like that.... Johny Cash's cover of NIN's Hurt.... Yeah, obvious... but still damn cool.

Sugar Ray did a fairly decent version of "Abracadabra". That´s one of my favourites. But like a couple of others here I can also vote for anything by Me First and The Gimme Gimmes.

twiztid - people are strange (doors cover)
radiohead - wish you were here (pink floyd cover)
sublime - no woman, no cry (marley cover)
ben harper - strawberry fields forever (beatles cover)
rage against the machine - fuck the police (nwa cover)
marilyn manson - another brick in the wall (pink floyd cover)

Fear Factory and Danzig - Enter Sandman (Metallica)
Sepultura - The Hunt (New Model Army, the original SUCKED)

Nirvana - Lake of fire
Gob - Paint it black
Manson - Sweet dreams
Metallica - Turn the page
Whitney Houston - I will always love you
I'm not a whitney fan but it was better than the original by big juggs.. I mean dolly...

/me goes to find some of these covers on Kazaa

If you like covers, you absolutely owe it to yourself to get the latest Johnny Cash CD. His cover of "Hurt" is fantastic, and he does "Bridge over Troubled Waters" with Fionna Apple backing him up. It's tearful. The only 'cringe' song is when he tries to do "Your Own Personal Jesus". Cash doesn't get early 90's British techno-pop. Otherwise it is definitely worth the purchase price / drive space.

jeff buckley - hallelujah.

word.

baaammmm! How could I have forgotten that one?

The Donnas' cover of Too Fast For Love is pretty funny.

I really dig The Happy Mondays' version of Step On, though I don't remember who did the original version.

My band (plug) just recorded a cover of Cry, Baby, Cry by The Beatles... I'm inclined to think it's good. ;)

Thraeryn was right with Type O's cover of Cinnamon Girl by Neil Young. It's fabulous.

I dont know who sings it but it is supposedly Phish covering Snoop Dogs Gin and Juice.

phish covering gin and juice is hilarious.

1. Metallica - Whiskey in the Jar (are we seeing a pattern here? :D)
2. Nonpoint - Evil Ways
3. Marilyn Manson - You Spin Me Right Round
4. Stabbing Westward - Bizzare Love Triangle
5. Cake - I Will Survive

more...
Ben Folds - Golden Slumbers
Ben Folds Five - Raindrops Keep Fallin On My Head (live)
Nixons - Rocketman
Rufus Wainwright - Across the Universe
The Normals - Fake Plastic Trees (live)
U2 - Unchained Melody (live)

but nothing will EVER top Dynamite Hack - Boyz in tha Hood :D:D:D

I agree with a couple that have been mentioned

Gary Jules - Mad World from Donnie Darco
New Found Glory - Neverending Story

Also, one I havent seen mentioned is
Goldfinger - 99 Red Ballons

Me and my friend cracked up the first time we heard dynamite hack boyz in the hood

Beatles' "Twist and Shout."

Eddie Vedder - Crazy Mary
Pearl Jam - Baba O'Riley
Dune - Who Want's to Live Forever

Tori Amos - Lovesong (Cure cover)

Goldfinger - 99 Red Balloons

or

Handbags And Galdrags - Stereophonics

Here's mine...

Foo Fighter's Baker Street.
Primus w/Ozzy NIB totally kicks
Limp Biz doing Sanitarium, don't like Limp, but that kicks. MTV Icon
Marilyn Manson The KKK took my baby away
Finally..
The Offspring I want to be sedated

welll...

Johnny Cash, Rusty Cage
Nine Inch Nails, Memorabila
Shampoo, Cars
Ozzy & one of the Zappa kids that eludes me..., Stayin' Alive

Senor Coconut's cover of Beat it. Or Smoke on the water. Or Riders on the storm. Hilarious :)

One more I forgot about, Devo doing Satisfaction. Now that is my all time fav...

Boys of Summer - The Ataris
Brown Eyed Girl - Everclear
I Will Survive - Cake

Rammstein - Das Modell
Kraftwerk made the original

Our Lady Peace has a pretty good Dear Prudence cover.
Man Who Sold the World by Nirvana is very well done.