Heller died at his Long Island home on Sunday night, according to his wife, Valerie.
Published in 1961 to mixed reviews, Catch-22 became a cult favorite before it was recognized as an American classic. It eventually sold more than 10 million copies in the United States alone.
Heller based the novel on his own experience as an Air Force enlistee during World War II. He was a bombardier in combat over Italy and flew 60 missions before he was discharged as a lieutenant at war's end.
Catch-22 is about trying to stay alive amid the insanity of war. Its anti-government, anti-military sentiments struck a chord with many readers during the Vietnam era.
The protagonist, Capt. John Yossarian, is a bombardier who tries to get himself declared crazy and grounded so he won't have to fly more combat missions. But he's foiled by regulations, which Doc Daneeka explains: "Anyone who wants to get out of combat duty isn't really crazy."
The phrase quickly entered the lexicon: The New Shorter Oxford English Dictionary (1993) defines Catch-22 as "a condition or consequence that precludes success, a dilemma where the victim cannot win."
"Everyone in my book accuses everyone else of being crazy," Heller once said. "Frankly, I think the whole society is nuts and the question is: what does a sane man do in an insane society?"
Catch-22 was made into a movie starring Alan Arkin and directed by Mike Nichols in 1970; Heller himself did a stage adaptation of the novel in 1973 and also published a sequel to it, Closing Time, in 1994.
Heller was among the great writers of the World War II generation, a group that included James Jones, Irwin Shaw, Norman Mailer and Kurt Vonnegut.
Born in Brooklyn's Coney Island on May 1, 1923, Heller attended public schools before enlisting at age 19. After the war he got a degree in English literature from New York University, a master's from Columbia, and studied at Oxford University under a Fulbright scholarship.
He taught at Penn State for two years, then worked as an advertising and promotion writer for magazines including Time, Look and McCall's.
During the 1960s, Heller also worked on several Hollywood screenplays and contributed to the television comedy series, McHale's Navy, writing under the pen name Max Orange.
He wrote his first play, We Bombed in New Haven, which ran for 86 performances on Broadway in 1968. With publication of his second novel, Something Happened in 1974, he devoted himself to writing full time.
Good as Gold followed in 1979, God Knows appeared in 1984. To interviewers who asked him about never having written another book s successful as his first, he answered: "Who has?"
In Closing Time, his sixth novel, Yossarian and his friends looked back on old acquaintances, former marriages and the Coney Island of Heller's own youth.
"When people our age speak of the war it is not of Vietnam but of the one that broke out more than half a century ago and swept in almost all the world," he wrote in the novel's opening sentence.
In 1981 Heller contracted Guillain-Barre syndrome, a neurological disorder that left him nearly paralyzed for six months. After lengthy therapy, and with the aid of his boyhood friend Speed Vogel, he largely recovered. They co-wrote a book about his ordeal, No Laughing Matter.
Heller liked to eat well and to listen to recordings by Count Basie and Lester Young. "I hate sports. I also hate gardening and walking. I don't go to movies or the theater or watch television," he once said. "What I do like is lying down."
Heller married Shirley Held in 1945 and they had a daughter, Erica, and a son, Ted. They divorced in 1984 and three years later he married Valerie Humphries, a nurse he met while recovering from his paralysis.