His other films include A Hatful of Rain (1957), Shake Hands with the Devil (1959, with James Cagney), One Foot in Hell (1960, with Alan Ladd), The Hoodlum Priest (1961), Advise & Consent (1962, with Henry Fonda and Charles Laughton), Baby the Rain Must Fall (1965, with Steve McQueen and Lee Remick), Conquest of the Planet of the Apes (1972), Deadly Hero (1975), and Peggy Sue Got Married (1986, with Kathleen Turner).

He was a member of the student government, glee club, and joined the Alpha Phi chapter of the Omega Gamma Delta Fraternity.

A member of the Church of the Brethren, Murray registered as a conscientious objector during the Korean War, when many young American men were being drafted into the armed forces.

His performance as the innocent cowboy who is determined to get Cherie was well received, and he was nominated for a BAFTA for Most Promising Newcomer and for the Academy Award for Best Supporting Actor.

Despite director Fred Zinnemann's intention to typecast the actor as the comical brother Polo, Murray insisted on playing the lead.

Murray starred as a blackmailed United States senator in Advise & Consent (1962), a film version of a Pulitzer Prize-winning novel by Allen Drury.

He also co-starred with Steve McQueen in Baby the Rain Must Fall (1965), and played the ape-hating Governor Breck in Conquest of the Planet of the Apes (1972).

He starred with Otis Young in the ABC western television series The Outcasts (1968–1969) featuring an interracial bounty hunter team in the post-Civil War West.