Randall died in his sleep Monday night at NYU Medical Center of complications from a long illness, according to his publicity firm, Springer Associates. The actor developed pneumonia after undergoing heart bypass surgery in December.
He is survived by his wife, Heather Harlan Randall, who made him a father for the first time at age 77, and their two children, 7-year-old Julia Laurette and 5-year-old Jefferson Salvini.
Randall was hospitalized after starring for a month in "Right You Are," a revival of Luigi Pirandello's play by the National Actors Theatre, which he founded.
In a tribute to the actor, known for his work on stage as well as television, lights at all the Broadway theaters were to be dimmed at 8 p.m. Tuesday.
Randall joked in September about how he envisioned his funeral: President Bush and Vice President Cheney would show up to pay their respects but they'd be turned away, because his family knows he didn't like them. During a speech to the National Funeral Directors Association, he said funerals should be planned as a celebration of life and "a touch of humor doesn't hurt a bit."
Randall won an Emmy for playing Unger on the sitcom based on Neil Simon's play and movie. The show ran from 1970-75, but Randall won after it had been canceled, prompting him to quip at the awards ceremony: "I'm so happy I won. Now if I only had a job."
The show's charm sprang from Randall's chemistry and conflict with Jack Klugman as sloppy sportswriter Oscar Madison, with whom he's forced to share an apartment after both men get divorced.
Before that, Randall was best known as the fastidious "best friend" figure in several Rock Hudson-Doris Day movies, including 1959's "Pillow Talk" and 1961's "Lover Come Back."
The actor became a fixture on David Letterman's late-night talk shows, appearing a record 70 times on the "Late Show" alone. He made fun of his own prim image by taking part in Letterman's wacky antics, including allowing himself to be covered in mud.
And in 1993, when Conan O'Brien took over the time slot at NBC that Letterman had vacated for a new show at CBS, Randall was a guest on O'Brien's debut episode.
After "The Odd Couple," Randall had two short-lived sitcoms, one of which was "The Tony Randall Show," in which he played a stuffy Philadelphia judge, from 1976-78.
From 1981-83, he played the title role in the sitcom "Love, Sidney," as a single, middle-aged commercial artist helping a female friend care for her young daughter.
The show was based on a TV movie in which Sidney was gay; in the TV show, the character's sexual orientation was implied, but never specified. This occurred more than a decade before the much-hyped coming-out on "Ellen" in 1997, which made Ellen DeGeneres' character the first openly gay central figure on a network series.
For his television work, Randall got a star on the Hollywood Walk of Fame in 1998.
In an effort to bring classic theater back to Broadway, Randall founded and was artistic director of the nonprofit National Actors Theatre in 1991, using $1 million of his own money and $2 million from corporations and foundations. The company's first production was a revival of Arthur Miller's "The Crucible," starring Martin Sheen and Michael York, which hadn't been staged on Broadway in 40 years.
The next year, Randall's production of Ibsen's "The Master Builder" didn't exactly draw raves. AP Drama Critic Michael Kuchwara called it "deadly earnest — and dull."
Subsequent performances included "Night Must Fall," "The Gin Game" and "The Sunshine Boys," in which Randall reunited with Klugman, in 1998. Randall also starred in his company's Tony Award-winning staging of "M. Butterfly."
The actor also was socially active, lobbying against smoking in public places, marching in Washington against apartheid in the '80s, and helping raise money for AIDS research in the '90s.
Born Leonard Rosenberg on Feb. 26, 1920, Randall was drawn as a teenager to roadshows that came through his hometown of Tulsa, Okla.
"One night, the entire town turned out to see the Ballet Russe de Monte Carlo perform Swan Lake and Sheherezade," he wrote. "I — and most of the audience — had never seen a ballet before. We stood and cheered, thinking it was a 'once in a lifetime' event."
Randall attended Northwestern University before heading to New York at 19, where he made his stage debut in 1941 in "The Circle of Chalk."
After Army service during World War II from 1942-46, he returned to New York, where he appeared on radio and early television. He got his start in movies in 1957.
He was married to his college sweetheart, Florence Randall, for 54 years until she died of cancer in 1992.
"I saw her in a bank — I never saw another girl in my life. She was gorgeous, the most beautiful girl I ever saw," Randall said in a TV interview in 1995.
Later that year, he married Harlan, who was 50 years his junior. Randall met her through his National Actors Theatre; former New York Mayor Rudolph Giuliani performed the ceremony.