From PEOPLE Magazine Click to enlarge
He famously sports one of Hollywood's biggest chins, but Jay Leno has refused to let his 17-year reign as King of Late Night give him a swelled head. "I'm a great believer in low self-esteem," says Leno, who steps down as host of The Tonight Show on May 29. "If you always assume you're the dumbest person in the room, you'll work a bit harder."

It's an approach that has served him well over 17 years and some 4,000 monologues as the comedian, 59, charmed audiences and A-listers alike with his laid-back, nice-guy demeanor. The secret to his success? "Try to have a relationship with everybody you make fun of, and be fair," he says. "You have to humiliate everybody equally—but like the Mafia, don't go after people's wives or children. Dogs are okay, though."

After a final week of shows featuring his favorite guests—including, he tells PEOPLE exclusively, Arnold Schwarzenegger, Billy Crystal and Mel Gibson—Leno will pass the Tonight torch to Conan O'Brien. ("I'm thrilled he's the one who got this," says Leno, whose biggest career regret is his falling out with David Letterman, who had also wanted to succeed Johnny Carson as Tonight Show host.) But he'll be back on NBC this fall, interviewing guests and telling jokes on The Jay Leno Show, which will air every weeknight at 10 p.m. Will he bring along Leno staples like "Jaywalking" and "Headlines"? "Anything that works, we'll keep," Leno says. "We'll see what happens." But first, he sat down with PEOPLE's Pamela Warrick to reflect on some of his most cherished memories.

1995
After Hugh Grant was caught with a prostitute, "he showed up that day alone with no entourage and said, 'I screwed up. Do what you have to do. Have your fun.' We had recently started [beating Letterman], and that was the capper."

2000
When Jason Sehorn got on his knee and proposed to Angie Harmon (as Elton John looked on), "that was a real moment," says Leno. "I knew he was going to do it—it's my show—but she didn't! It was a lot of fun."

1995
"The Dancing Itos—it was my idea," Leno says of the routine prompted by O.J. Simpson's "ridiculous trial—everybody was preening for the cameras. But Judge Ito still drops me notes. He's a very nice man."

2009
"It's not like he's saying, 'I hope Jay asks me on the show!'" Leno says of President Obama's recent visit. "I think it had something to do with my free shows in Detroit [for the unemployed]."

1987
"[The Tonight Show] guys didn't believe me that I was the Sexiest Man Alive," he says of his PEOPLE cover, which he kept framed in his office near the set. "So what if it was 'Just kidding'? It was fun and very amusing."