Zanuck had a huge influence on Hollywood, as a former head of production at 20th Century Fox and as a producer for the last 40 years.
With Fox, he had hits such as Butch Cassidy and the Sundance Kid and MASH, before being fired by his own father over disasters like 1967's Doctor Dolittle.
His Zanuck/Brown film company, which he later created with David Brown, is credited with giving an early chance to Spielberg, who made Sugarland Express and Jaws with the producers. Jaws was Zanuck's first best picture Oscar nomination, in 1975.
'A very fine producer'
"He taught me everything I know about producing. He was one of the most honourable and loyal men of our profession and he fought tooth and nail for his directors," Spielberg said Friday in a statement.
Zanuck and Brown also made the Academy Award-winning The Sting in 1973, and went on to produce the box-office hit Cocoon in 1985 before dissolving their partnership three years later.
The next year, Zanuck's new venture released Driving Miss Daisy, which won him a best-picture Oscar, as well as a best-actress award for Jessica Tandy and the trophy for best adapted screenplay.
"Richard was a good and longtime friend," said Morgan Freeman, who co-starred with Tandy in the film. "A very fine producer who was wonderful to work for and with."
Zanuck, born in 1934, spent much of his childhood at Fox studios, which his mercurial father, Darryl, ran from the 1930s until the early '70s. "When I was a kid I was playing hide-and-seek on the movie back lot," Richard Zanuck once recalled.
The elder Zanuck appointed his son production chief in the early 1960s. His reign brought one huge hit, The Sound of Music, but such other so-so films as Crack in the Mirror, William Faulkner's Sanctuary and Star!
As the studio began to flounder when the big-budget movie musical era died, Darryl Zanuck, under pressure from the board of directors, fired his son in 1970 in an effort to save his own job. But the manoeuvre failed and he soon followed his son out the door.
The dismissal shattered the soft-spoken younger Zanuck, and it was not until shortly before his father's death in 1979 that the pair resolved their differences.
"It was different from the usual father-son relationship," Zanuck told the New York Times in 2003. "But I was able to patch everything up before my father died."