“Crossroads” by Cream blows both “Crossroads Blues” and “Travelling Riverside Blues” by Robert Johnson away.
cough
sputter
I am reminded of a scene from Ghost World.
Joss Stoves cover of “Fell in Love with a Girl” (boy in her version) by the white stripes, I like both but her version is just plain sexy
http://www.youtube.com/watch?v=wDU2EXsW9tA (Joss’s version)
http://www.youtube.com/watch?v=XRDi67G0Siw (The original)
Aretha Franklin’s version of Respect over Otis Redding’s original.
Better than the Beatles:
Earth, Wind and Fire’s version of Got to Get You Into My Life.
John Denver’s version of Mother Nature’s Son.
Veruca Salt’s cover of “My Sharona” is awesome. (Possibly NSFW, as the video itself is Kate Moss in lingerie doing some rather mediocre pole dancing,)
That’s always the first song that comes to my mind in threads like this. Jules’ version fits the music to the lyrics perfectly. It makes my wife cry. 
You know, I’m gonna have to go with David Cook’s studio version of Billie Jean. Michael Jackson’s was catchy and all, and Chris Cornell’s arrangement proved what the song could be, but David made it hauntingly beautiful.
I almost puked during that! My wife and I were rolling around on the couch wincing in pain! Ok, she wasn’t, but she’s not nearly as dramatic as me. She was cringing though, I swear.
Another one I just thought of is ‘Country Roads, Take Me Home’ by Toots & the Maytals. Superior to John Denver’s IMO, though I like them both.
…and I’ll add that their version of “Pressure Drop” tops the Toots original.
I think Sleeper’s version of “Atomic” is marginally better than the Blondie original.
I can’t usually bear to listen to Rod Stewart, even a good song like “Maggie May,” so thank God Blur covered it and crushed his original.
Weird, I like the Clash and I didn’t know they did Pressure Drop. Neville from the Specials told me personally that it’s the most covered ska song ever, so I’m not surprised.
Violent nastiness upon ALL who question the Beatles’ superiority!
ahem Manford Mann did much better covers of Bruce Springsteen than Springsteen could have done himself. Also, Joan Jett and the Blackhearts thouroughly put the proper amount of scandal into Crimson and Clover.
Along the same vein, “Black Magic Woman” by Santana is much better than the original Fleetwood Mac version.
I prefer their cover ofHelter Skelter as well.
Bah! Bah, I say!
Manfred Mann’s “Blinded by the Light” is limp and pathetic next to the Boss’s original.
Besides which, Manfred Mann gets the lyrics wrong.
You Keep Me Hanging On- I like the Vanilla Fudge version better than the Supremes.
Zenith, are you thinking of the Motley Crue version of Helter Skelter (which I prefer)? I am not aware of Aerosmith doing this one. While I’m at it, I’ll add that I like Aerosmith’s version of “Come Together” over the Fab Four’s version (not that it’s bad, mind you).
Please tell me this is either a whoosh, or that you mean that Oingo Boingo’s cover of “You Really Got Me” is better than Van Halen’s cover of the same, not that the Van Halen version is the original.
I’m assuming that the joke is that “Satisfaction” by the Rolling Stones is actually a cover of Otis Redding’s version.
John Lennon’s cover of “Stand By Me” is the definitive version for me.
Most of mine have already been mentioned, but:
Hurt by Johnny Cash
Tainted Love by Marilyn Manson
Personal Jesus by Marilyn Manson (is this a cover, or the original? I’m not sure)
Mad World by Gary Jules
Tragedy by Celldweller (just heard this one recently, and It’s a big improvement over the BeeGee’s version (which I also liked))
Just to be a bit different I like Pearl Jam’s version of Last Kiss better then the original it is a slower song that makes it much sadder then the original, which I like as well.