But his long experience with fame hasn't always been happy.
"It's dust to me," Clapton said. "I don't think fame has any substance. So it doesn't have any interest to me. In fact, I think it's quite a dangerous commodity and very destructive."
That may help explain why on his new CD, "The Road to Escondido," which comes out this week, Clapton teamed up with a man who has spent 40 years trying not to be famous: songwriter and guitarist J.J. Cale.
"When they say, 'Well, you gotta do some interviews on TV,' I went, 'Oh, I like to watch TV, but I don't wanna be on it,'" Cale told Sunday Morning correspondent John Blackstone. "I guess I'm gonna be on it."
By his own choice, Cale has avoided the spotlight. Clapton had to push him into it.
"He was great initially, but then ... you could feel him kind of shuffling backwards out of the room all the time," Clapton said.
Cale was just a struggling songwriter out of Tulsa, Ok., and Clapton was already a superstar when he recorded one of Cale's songs, "After Midnight." It became one of Clapton's biggest hits.
"A buddy of mine called up and says, 'Well ... Eric Clapton's cut your tune,' You got a hit on your hands. Come down to Nashville and make an album,'" Cale said. "And I said, 'An album. What is that?' I come from the old, you know, you make one song. Right? He said, 'Oh, no. You gotta put 10 or 12.' I said, 'I ain't got 10 or 12 songs. That was it.' You know?"
Clapton didn't know Cale was offered a record deal after "After Midnight" came out, and said: "Isn't that funny."
Cale was just being modest. He did have more songs and in 1977 Clapton recorded another one: "Cocaine."
"I didn't really wanna know what he meant, except that at the time I was very pro-cocaine," Clapton said. "When I listened to it a little more, when I got into recovery and stopped doing all this stuff, I chose to believe it was anti-cocaine. Maybe it's ambivalent."
After that hit, Cale's life changed a bit.
"They sent money to me," he said.
Though most of Clapton's millions of fans didn't have a clue, throughout his career Cale was a constant muse, inspiring songs like "Lay Down Sally."
"It's a very difficult thing to describe," Clapton said. "It's an R&B thing. What it is I think is, he's taken elements of R&B and blues and mixed 'em up with country."