I was having a discussion with some friends last night about bands which never have recorded a cover song.
Genesis is the first band that came to mind. On a couple of tours, they did play a medley of classic rock songs, but this was never released on a CD.
I’m sure there must other major rock bands which have never recorded a cover song. I just can’t think of any!
Dire Straits?
The Beatles?
Assuming you’re not joking, their first 4-5 albums had cover songs on them.
Led Zep
Kiss
Kansas
Boston
Bon Jovi (I don’t think “The Boys are back in town” was put on an album)
From the AMG (the song “You Shook Me”):
Also, KISS did a cover of Bobby Rydel’s “Kissin’ Time” on their first album.
What are you talking about? They did a cover of Poison’s I Wanna Rock and Roll ! 
I just looked it up. Willie Dixon also gets credit for “I Can’t Quit You Baby”.
OK, but I’m correct about Bon Jovi, right?
If this thread had been posted a month earlier, I would have said Rush.
Kansas did “Eleanor Rigby” on their 1998 Always Never the Same.
It appears that Bon Jovi has not done any covers, though.
Ooops, Bon Jovi did Tom Waits’ “Just Older” on their “Crush” album. I wanna get one right dammit!
I still got a chance with Boston (if they’re considered a major rock band).
Velvet Revolver
I checked them, too. It’s pretty much Tom Scholz on nearly every song.
They were considered a major rock band in the 70s.
Zeps “Whole Lotta Love” is a cover of the Small Faces,“You Need Lovin”
Buffalo Springfield…with composers like Steven Stills,Neil Young & Ritchie Furay,
No Covers Necessary
Wow, I never knew that about “Whole Lotta Love”. Cool. You can hear a clip here
As far as I know, the only cover Queen ever recorded was the British national anthem, “God Save the Queen.”
King Crimson didn’t record any cover tunes for 30 years, but finally broke down and recorded a cover of John Lennon’s “Free as a Bird.”