"Bus Stop" (1956) provided Murray with a strong role as a naive, yet forceful, cowboy romancing a singer (Marilyn Monroe). For his efforts, the actor earned an Oscar nod as Best Supporting Actor. His two subsequent features, "The Bachelor Party" and "A Hatful of Rain" (1957) both provided meaty roles, but later efforts failed to capitalize on his early promise. Murray moved into producing and screenwriting with "The Hoodlum Priest" (1961), a true story about a clergyman who worked with criminals, in which he also starred. His 1970 directing debut, "The Cross and the Switchblade", was an earnest but uneven feature. A second feature, "Damien" (1977), a biopic of the priest who worked with lepers in Hawaii, has never been released theatrically. The 80s saw Murray in mostly paternal roles (e.g., "Endless Love" 1981; "Peggy Sue Got Married" 1986).

Murray has been a constant fixture on TV since the late 50s. He served as a celebrity panelist on "Made in America" (CBS, 1964) and starred in the Western series "The Outcasts" (ABC, 1968-69). TV viewers may remember him from the first two seasons of the CBS primetime soap "Knots Landing" (1979-81) as Michelle Lee's husband. Two later series, "Brand New Life" (NBC, 1989-90) and "Sons and Daughters" (CBS, 1991) were both short-lived. In his TV-movies, Murray has generally been cast in stalwart roles, generally as politicians or businessmen.

From 1956 to 1961, Murray was married to his "Bus Stop" co-star Hope Lange.