Rickles was a young comic in the late 1950s, building a reputation for himself at Miami Beach nightclub Murray Franklin's, when he first encountered the Chairman of the Board.
Sinatra, who was appearing down the street at the famous Fontainebleau Hotel, walked in one night while Rickles was on stage. The comedian saw him and said, "Make yourself at home, Frank. Hit somebody."
"He laughed like crazy," Rickles said. "We became great friends. We always had a good time. He loved my attitude and humor. He was amazingly loyal. That's what I loved about him. He had a tough side, but he would do anything if he was your friend. When he walked into a restaurant, everything would stop. He had such great charisma."
Though his ironic nickname is "Mr. Warmth" because of his caustic humor, in reality Rickles is a pussycat. Over coffee at a Beverly Hills hotel lounge recently, Rickles couldn't be nicer. He's 87 now and as sharp as ever. His back isn't in the best of shape, but that doesn't stop him from making 25 to 50 stand-up appearances a year. In fact, he's been a mainstay in Las Vegas since 1959.
"My wife, Barbara, is great," he said. "She arranges when I do work that I have a day off between performances."
Rickles has been in New York this week doing David Letterman and two stand-up gigs, including one Saturday night in Westbury, N.Y., with Regis Philbin. On Monday, he's receiving the Friars Club Lifetime Achievement Award for Comedy at a gala at the Waldorf Astoria. Among those scheduled to honor Rickles are his good friend Bob Newhart, Philbin, Kathy Griffin, John Mayer and Diana Krall.
He's no stranger to the famed private club known for its ribald roasts of actors and comedians. Rickles was roasted by the club in 1968, and his picture hangs on the club's wall of fame. He was also one of the frequent guests on the sanitized "Dean Martin Celebrity Roasts" that aired on NBC in the 1970s.
But unlike the roasts, the gala is much more circumspect to the honoree.
Bruce Charet, the "Scribe" of the club, said that Rickles is of the "generation that made the Friars famous. He is sort of the last man standing from the Rat Pack-Sinatra generation. He's truly one of the greats from that generation and has become an iconic figure for two generations that have come after him. He is the coolest 87-year-old man on the planet."
In fact, Rickles has never gone out of style. He earned an Emmy five years ago for John Landis' HBO documentary "Mr. Warmth: The Don Rickles Project." He's known to children far and wide as the voice of Mr. Potato Head in the "Toy Story" blockbusters. He even worked with director Martin Scorsese and Robert De Niro in 1995's "Casino."
Rickles has gone high-tech. He has his own app and more than 115,000 followers on Twitter. "I write my own tweets," he says.
Rickles didn't set out to become a comedian. After serving in the U.S. Navy in the Philippines in World War II, he attended the American Academy of Dramatic Art in New York with fellow students Grace Kelly, Jason Robards and Anne Bancroft.
"I started to get a bit of television," he said. "I was always making the rounds, but I could never get to Broadway."
So he turned to comedy. And in those early years, he appeared in more than a few dives.
"I played one place called the High Hat or the Tip Top, and the boss used to sit in the front in his bathrobe and spit on the floor while I was working," he said. "That will give you an idea of the places I played. You always had to dress in the kitchen."
He started out doing jokes and impersonations but never really enjoyed the latter because so many other comics were doing it.
"All of a sudden -- it wasn't planned -- I would get through doing some impersonations and [I'd see] someone sitting in the audience. I would say, ‘Charlie, the tie. Please take the tie off. You're making a jerk of yourself.' I started talking to the audience and then my style developed. I have things I always say and things I never said before in my life."
And he's always written his material.
"If something strikes me as funny, I'll put it in my performance. I always have a beginning, a middle and an end, but in between it changes."
Just as he was making his mark as a comic, Rickles did get some decent acting roles -- making his film debut in Robert Wise's 1958 World War II submarine drama "Run Silent, Run Deep" with Clark Gable and Burt Lancaster.
"Gable was great," he said. "We had a lot of fun. When he came out of his trailer, he would be in a Brooks Brothers suit and a tie. People used to stand in line to see him get in his car! The magic of a star in those days. It was completely different."