Yeah, that's right.

Off the top of my head-

Jeff Buckley-Hallelujah (L. Cohen)

Three Dog Night- Mama Told Me Not to Come (R. Newman)

Not that these are shining examples, but they'll do.

Some of Johnny Cash's covers also come to mind.

Sorry to go tangential on the first reply, but can I vote for the Slits' cover of "I Heard It Through The Grapevine" as the only cover of an incredible and formally 'classic' song that is as good as the original? - though in the most utterly different way. The best cover in the world. The unalterable perfection of the original makes the pairing unique. Doesn't it?

I think it just depends on which you heard first, usually.

I guess Aretha Franklin's cover of "Respect" totally eclipsed the original.

I suspect that Metallica's covers of NWOBrrrrrrrritishHM better the originals. Of course, maybe I should actually listen to Angelwytch before I pronounce judgement.

Also, Killdozer's cover of "Stranglehold" was, dare I say, sublime?

Born Against-I'm not an idiot (screeching weasel)
Nirvana-Man who sold the world (bowie)
Devo-Satisfaction (stones)

I'll second the Devo one... how 'bout the Raincoats' "Lola" ?

But I'll have to wholeheartedly disagree with that vocal wanker Buckley's version of the Cohen song. His voice is the equivalent of watching some shitty 21st century blues solo jam by white dudes.

"All Along The Watchtower" - Hendrix

Toots and the Maytals' cover of John Denver's "Country Road" is one of my favorites.

I guess this counts as a cover cover or maybe it's a pseudo cover but Pavement's cover of "Secret Knowledge of Backroads" totally dwarfs the original by Silver Jews.

Dinosaur Jr - Just Like Heaven (the Cure song)

ginandtacos.com wrote:Dinosaur Jr - Just Like Heaven (the Cure song)

I've gotta give Dinosaur the nod over Frampton on "Show Me the Way," too.

Also:

Nina Simone: "Just Like Tom Thumb's Blues"
Jackson 5: "Doctor My Eyes"
Rick Nelson: "She Belongs to Me"
Eric Burdon & War: "A Day in the Life"
Thin Lizzy: "Rosalie"
Jimi Hendrix: "Hey Joe"
Minor Threat: "12XU"
The Everly Brothers: "Sing Me Back Home"
Waylon Jennings & Jessi Colter: "Bridge Over Troubled Water"
Melanie: "Carolina in My Mind"