A familiar character actor, the tall, burly Kennedy began his career as a child performer on stage and in radio performances. After a stint in the Army during WWII, during which he was responsible for the opening of the first Army Information Office that provided technical assistance to films and TV shows, he earned a spot as a technical advisor on "The Phil Silvers Show/Sgt. Bilko". Kennedy went on to appear as either a villain or hero in a variety of guest appearances ("Have Gun, Will Travel"; "Cheyenne"; "Gunsmoke") and TV-movies and miniseries ("See How They Run" NBC, 1966; "Deliver Us From Evil" ABC, 1973; "Backstairs at the White House" NBC, 1979). He headlined the short-lived police dramas "Sarge" (NBC, 1971-72), as a former cop turned priest, and "The Blue Knight" (CBS, 1975-76), as a foot patrolman. Kennedy hosted the short-lived public affairs show "Counterattack: Crime in America" (ABC, 1982), a forerunner of shows like "America's Most Wanted". In 1988, he joined the cast of the long-running CBS serial "Dallas" as Carter McKay, a business rival of the Ewing brothers (Larry Hagman and Patrick Duffy).
Kennedy began his film career in 1961 in "Little Shepard of Kingdom Come" and went on to menace Audrey Hepburn in "Charade" (1963), was a member of "The Dirty Dozen" (1967) and won the 1967 Best Supporting Actor Oscar as prisoner on a chain gang with Paul Newman in "Cool Hand Luke". He provided stoic support in "disaster movies" like "Airport" (1970) and "Earthquake" (1974) and was Leslie Nielsen's partner in comedy in "Naked Gun - From the Files of Police Squad!" (1988) and its two sequels. Kennedy also won praise for portraying himself performing scenes from a low-budget sci-fi film in Albert Brooks' "Modern Romance" (1981).