With Clapton, I think it depends on the era the listener has focused in on. Alot of people would certainly deem "Wonderful Tonight" or "Tears in Heaven" as prime candidates for his signature song, but I'd agree with Layla.
I'd say U2 would be better fitted with "One" or "Still Haven't Found What I'm Looking For".
For the Eagles, "Lyin' Eyes" wouldn't be scoffed at, but Hotel California is pretty much it. For Elton John I'd probably hazard "Sacrifice".

As for others...
RHCP's - Under the Bridge
Guns n Roses - Sweet Child
Jeff Buckley - Hallelujah
Radiohead - Paranoid Andrioid
Green Day - Basket Case
The Kinks - You Really Got Me
Michael Jackson - Thriller
Oasis - Wonderwall
Fleetwood Mac - Little Lies
David Bowie - Heroes
Dire Straits - Walk of Life
Duran Duran - Rio