Jeff Bridges isn’t like other leading men. So goes the tale for over 50 years and 70 films. Where other actors of his generation—Robert De Niro, Jack Nicholson—brought volume and bravado, Bridges excelled in the shadows. A charming pretty boy turned weary and soulful iconoclast, his characters have never been showy. As The Dude in “The Big Lebowski” or Bad Blake in “Crazy Heart,” he’s moved into his roles and lived in them—“enough,” as one critic wrote as early as 1973, “to make a picture worth seeing.”

“I’m not sure what to make of all that,” Bridges told Variety at Film at Lincoln Center Monday evening, where the actor received the prestigious Chaplin Award. “It’s shocking for myself to think about how many films I’ve done,” he said. “Each film is like a little lifetime. I was a reluctant actor at first. It took many...