Covers Project is a superb site for looking up covers and original artists, and quite a few songs that you might think were originals are actually covers. Led Zeppelin covered a LOT of songs, in the blues tradtion. Notably Stairway to Heaven's acoustic intro is actually borrowed from a song called Taurus by Spirit.
Some quick Led Zeppelin covers:
Babe I'm Gonna Leave You
Dazed and Confused
The Lemon Song
Gallow's Pole
In My Time of Dying
My guess as to a band who never covered would be Steve Miller Band. Alas, I just checked on coversproject and apparantly they have covered a bunch of songs as well.