King's X - Manic Depression
Rollins Band - Are You Ready
Metallica - Breadfan
Van Halen - You Really Got Me

Type O Negative - Summer Breeze (Seals & Croft cover)

Korn - Wicked (orig. Ice Cube)

Gold Dust Woman - Hole (Fleetwood Mac)
Across the Universe - Fiona Apple (The Beatles)
Heroes - The Wallflowers (David Bowie)
I Will Always Love You - Whitney Houston (Dolly Parton)
Sweet Child O Mine - Sheryl Crow (Guns N Roses)

Dick Dale - Ring of Fire (Johnny Cash, et all)

I would have to vote for this being the most outstanding cover/remake.

Oasis also does a pretty respectable version of Bowie's "Heroes". It's on the B-side of their "Do You Know What I Mean" single. Noel sings it.

NoFX - "Gin and Juice" (Snoop Doggy Dogg orig.)

Me First and the Gimme Gimmes - "Only the Good Die Young" (Billy Joel orig.)

Nerf Herder - "Kiss Me Deadly" (Lita Ford orig.)

I put in my vote for Hells Bells covered by the Dandy Warhols.

Sweet tune, funny hereing an AcDc song you here in stadiums to get the crowd pumped up all chilled down.

The Man Who Sold the World - Nirvana (david bowie cover)

I Fought the Law - The Clash

Most of Rasputina's covers I like better than the originals, but that's cuz I like Rasputina I guess and don't much care for most of the people they cover... cept for Pink Floyd of course. Maybe it's the cellos that do it for me.

~Scheherazade

The Sundays - Wild Horses (Rolling Stones)

Tori Amos - all of "Strange Little Girls" actually
but in particular:
"Its Raining Blood" originally by Slayer

yeah but Bowie's is so much better (I really like the Nirvana version too, though)

Elvis Presley's versions of "My way" and "Bridge over troubled water"

The song was written for Frank and then perfected by the king..of course thats just my opinion..
I love Frank..but Elvis' version is so much more powerful

A Perfect Circle - Diary of a Lovesong (combination of Ozzie's Diary of a Madman and the Cure's Lovesong)

9353 - Born to be Wild

nobody's mentioned:

Cowboy Junkies "Sweet Jane" (orig. by Velvet Underground)

-di doctor-

Bobby Fuller Four - I Fought The Law (The Crickets)
The Quakes - Behind The Wheel (Depeche Mode)

.


I thought Rufus' version of "across the universe" was terrific..
Blows the beatles version out of the water...

I think Im gonna say
Cum on feel the noize-quiet riot
Mama were all crazee now-quiet riot
Wild world-Mr. Big

I love the Stereophonics version of Handbags and Gladrags but to be honest it sounds the same as when Rod Stewart did it.

Hard to say that these covers are "better" than the originals since some of the originals are classics, but without repeating any cover versions previously mentioned in this thread, here are some pretty decent renderings.

Clash - Pressure Drop (Toots & the Maytals)
Cud - Lola (The Kinks)
Feelies - Paint It Black (Rolling Stones)
Feelies - What Goes On (Velvet Underground)
Hunters and Collectors - Throw Your Arms Around Me (Neil Finn/Split Enz)
Ike & Tina Turner - Honky Tonk Woman (Rolling Stones)
Lick the Tins - Can't Help Falling in Love (Elvis Presley)
Liz Phair - Turning Japanese (The Vapors)
Lucinda Williams - Return of the Grievous Angel (Gram Parsons)
Otis Redding - Satisfaction (Rolling Stones)
Poi Dog Pondering - Going up the Country (Canned Heat)
Poi Dog Pondering - Love Vigilantes (New Order)
REM - Pale Blue Eyes (Velvet Underground)
Shonen Knife - Top of the World (The Carpenters)
Yung Wu - Powderfinger (Neil Young)
Drugstore - Old Shoes (Tom Waits)

Tom Jones--Kiss