Barry died in New York, where he had lived for some time, on Sunday, his family said. The family did not release the cause of death.
Though his work on the Bond films is among his most famous, the English-born composer wrote a long list of scores, including for "Midnight Cowboy," "Dances with Wolves" and "Body Heat." He was proud of writing both for big action blockbusters and smaller films.
He won two Oscars for "Born Free" in 1966, for best score and best song. He also earned statuettes for the scores to "The Lion in Winter" (1968), "Out of Africa" (1985) and "Dances with Wolves" (1990).
His association with Agent 007 began with "Dr. No" in 1962, although his contribution to that film was not credited and is in dispute.
Monty Norman, who was credited as the composer for "Dr. No," sued The Sunday Times in 2001 for reporting that Barry had composed the theme, working from scraps of Norman's work. Norman won the case, collecting 30,000 pounds ($48,000).
Barry testified that he was paid 250 pounds to work on the theme music, developing the guitar line from part of Norman's song "Bad Sign, Good Sign," but agreed that Norman would get the credit. He was asked whether Norman wrote the theme and responded "absolutely not."
In later years, Barry limited his comment on the case to saying, "If I didn't write it, why did they ask me to do the other ones?"
He subsequently wrote music for "Goldfinger," "From Russia with Love," "Thunderball," "You Only Live Twice," "On Her Majesty's Secret Service," "Diamonds are Forever," "The Man with the Golden Gun," "Moonraker," "Octopussy," "A View to a Kill" and "The Living Daylights."
Born John Barry Prendergast, he recalled growing up "exposed to the fantasy life of Hollywood" at the eight theaters his father owned in Northern England.
"Rather than talkie-talkie movies, I liked films with excitement and adventure, because they were the ones that had the music," Barry said in an interview with The Guardian newspaper in 1999.
"It was nice to have the very commercial Bondian thing ... and then at the same time have these smaller movies which were artistically more interesting to do," he said.
Other films included "Robin and Marian," "Somewhere in Time," "The Cotton Club," "Peggy Sue Got Married" and "Howard the Duck." He was also nominated for Oscars for his scores of "Mary, Queen of Scots" in 1971 and "Chaplin" in 1992.
Barry trained as a pianist, studied counterpoint with York cathedral organist Francis Jackson, and later took up the trumpet. He founded a jazz group, the John Barry Seven, in 1957.
The group teamed with singer Adam Faith, scoring hits with "What Do You Want?" and "Poor Me," and Barry moved into film work when Faith was tapped to star in "Beat Girl" (titled "Living for Kicks" in the United States).
"The James Bond movies came because we were successful in the pop music world, with a couple of big instrumental hits. They thought I knew how to write instrumental hit music," Barry said in an interview with The Associated Press in 1991.
In an interview in 2008 with The Irish Times, Barry said his success "was not that difficult."
"If you hit the right formula, if you have an instinct for music, if you apply it, if you have the good fortune to meet with certain people who teach you well ... I didn't find it all that difficult," he said.
Barry was divorced three times. He is survived by his wife Laurie, his four children and five grandchildren. A private funeral was planned, the family said.