Melnick, who had recently undergone surgery for lung cancer, died Tuesday of multiple ailments at his home in Los Angeles, said his son, Peter.
"He was an extraordinary producer and an extraordinary executive," Sherry Lansing, a former studio executive whom Melnick mentored, told The Times on Wednesday. "He always thought out of the box and was never afraid to take a risk. His films stand the test of time."
Inspired by the success of James Bond movies, Melnick made his mark on popular culture with the enduring television hit he produced -- the 1960s spy-spoof series "Get Smart" that starred Don Adams as bumbling secret agent Maxwell Smart.
"James Bond and Inspector Clouseau -- those are the two biggest hits out there. Take a hint," Melnick told his writers, Buck Henry and Mel Brooks, according to a 2008 article in the Santa Fe New Mexican.
"Get Smart" won several Emmy Awards but Melnick received his in 1966 for producing "Ages of Man," which featured John Gielgud in a Shakespearean turn, and in 1967 for a presentation of "Death of a Salesman." Melnick shared his Emmys with producing partner David Susskind.
The first film Melnick produced was Sam Peckinpah's violent and controversial "Straw Dogs." Released in 1971, it led to Melnick being offered a job at MGM, his son said.
After joining the studio in 1972, Melnick rose to head of worldwide production, mining the vaults to help create the "That's Entertainment" greatest hits franchise.
He also oversaw such films as the Neil Simon comedy "The Sunshine Boys" and "Network," the 1976 biting satire of television that foreshadowed the ensuing decades.
While in charge of production at Columbia in the late 1970s, he helped develop the divorce drama "Kramer vs. Kramer," the nuclear drama "The China Syndrome" and the violent "Midnight Express."
For nine months in 1978, Melnick served as president of Columbia after studio president David Begelman was ousted in an embezzlement scandal.
The next year, Melnick produced Bob Fosse's "All That Jazz," which earned praise for experimenting with the musical genre, and followed it with 1980's "Altered States," a sci-fi horror film that starred William Hurt.
Melnick returned to musicals with 1984's "Footloose," about a teen's irrepressible need to dance.
While Melnick was making "Roxanne," the 1987 comedy that starred Steve Martin and updated the story of Cyrano de Bergerac, the pair had lengthy conversations about life, Melnick later recalled. They led Martin to write 1991's "L.A. Story," which Melnick produced.
He also worked on the groundbreaking "Making Love," a 1982 film about a man who leaves his wife for another man.
"Everyone was absolutely terrified it would hurt their careers," Melnick said in the New York Times in 1997 of trying to cast the male lead. "We finally cast Harry Hamlin . . . and I had to spend a lot of time persuading him that it wouldn't damage his career any more than Jimmy Cagney playing a damaged murderer damaged his.
"We were flying in the face of one of the last taboos," he said.
Regarding his approach to filmmaking, Melnick told the New York Times in 1990: "What I try to do is identify and work with the most talented people I can get."
He was born April 21, 1932, in New York City to Benjamin and Celia Melnick. His father, a Russian immigrant, died after a car crash when his son was 9.