Tool - No Quarter (Original by Led Zeppelin)
Great shout! I've noticed a fair few Nirvana songs mentioned, but 2 that have been overlooked for me are "In the Pines" (trad. American folk, but Kurt credits it to Lead Belly) and "Oh Me" (Meat Puppets). Both are on Unplugged album.
I am a huge Jerry Garcia fan, so I'd like to throw a few of his arrangements of classic tunes into the mix. NOT that they are better (well some are) but he always makes a song his own when he covers it:
After Midnight (JJ Cale) - Clapton's version is amazing as well
The Way You Do The Things You Do (Smokey Robinson, Robert Rogers)
Simple Twist Of Fate (Dylan)
Tangled Up In Blue (Dylan)
It Takes A Lot To Laugh, It Takes A Train To Cry (Dylan)
Dear Prudence (Lennon/McCartney)
I've Been All Around This World (Trad.)
Stealin (Trad.)
Man Of Constant Sorrow (Trad.)
and for me these 2 are better than the originals:
Deep Elem Blues (Trad.)
That's What Love Will Make You Do (James Banks, Eddy Marion, Henderson Thigpen)
Sorry for that, but I couldn't have Jerry go unmentioned.
A few covers that are better than the original:
Smashing Pumpkins - Landslide (Stevie Nicks)
Tegan and Sara - Walking With A Ghost (The White Stripes)
Albert King - Stormy Monday (T-Bone Walker)
Eric Clapton - Cocaine (JJ Cale)
Sublime - Jailhouse (Bob Marley)
Led Zeppelin - Babe, I'm Gonna Leave You (Joan Baez)
...sorry
I'll stop now.