Plimpton, a best-selling author who wrote about sports from a participant's point of view and edited the Paris Review literary journal, died in his sleep at his New York apartment on Thursday night, according to his lawyer, James Goodale.
"Last night, the 50th anniversary issue [of the Paris Review] was put to bed with him at the helm," said Mr Goodale.
"He had had some heart problems, but he seemed to be in very good health and we are all surprised by his death."
Educated at Exeter, Harvard and Cambridge, Plimpton was at home in literary circles, high society and sports arenas alike, writing for magazines and acting in films. He sailed with John Kennedy, played tennis with former president George Bush and flew on Air Force One with President Bill Clinton.
Over the years he appeared in numerous films, including Reds and Good Will Hunting, and even featured in an episode of The Simpsons, playing a professor who runs a spelling bee.
But Plimpton - a patron to Philip Roth and Jack Kerouac - was best known for writing about professional sports by taking part in the activities as an amateur.
In his first exploit, in 1959, he boxed three rounds with light-heavyweight champion Archie Moore and wrote books such as Out of My League (1961), about baseball, Paper Lion (1966), about playing football with the Detroit Lions and The Bogey Man (1968), about professional golf.
Allowed briefly to play quarterback for the Lions, he remembered the crowd cheering as he left the field after a series of mishaps.
"I thought about the applause afterward. Some of it was, perhaps, in appreciation of the lunacy of my participation and for the fortitude it took to do it," he wrote, "but most of it, even if subconscious, I decided was in relief that I had done as badly as I had."
Ernest Hemingway called Out of My League "beautifully observed and incredibly conceived".
"There are people who would perhaps call me a dilettante, because it looks as though I'm having too much fun. I have never been convinced there's anything inherently wrong in having fun," Plimpton once said.