Among Martin's memorable performances is his portrayal of the warden or "captain" of a state prison camp in the 1967 film Cool Hand Luke, in which he utters the line, "What we've got here is failure to communicate.

Martin also portrays a man with learning difficulties in "Cooter", an episode written by Sam Peckinpah in 1956 for the second season of the long-running Western series Gunsmoke.

In 1959, Martin played Polk, with Denver Pyle as Houston, in the episode "No Place to Stop" of the CBS Western series, The Texan, starring Rory Calhoun as Bill Longley.

[5]: 408  In another 1959 Western series, Martin was cast as Deputy Jess in the episode "Johnny Yuma" of ABC's The Rebel, starring Nick Adams.

In 1962, he was cast as Harold Horton in "The Chocolate Cake Caper" of the CBS sitcom, Pete and Gladys, starring Harry Morgan and Cara Williams.

In 1966, Martin appeared twice as "Cousin Fletch" in the short-lived ABC comedy Western The Rounders, with Ron Hayes, Patrick Wayne, and Chill Wills.

In 1967, Martin played Arizona miner Ed Schieffelin in the episode "Silver Tombstone" of the syndicated television series Death Valley Days.

In 1967, the same year as his role in Cool Hand Luke, he appeared in the episode "A Mighty Hunter Before the Lord" of NBC's The Road West series starring Barry Sullivan.

He also had a pronounced physical and vocal resemblance to playwright Tennessee Williams and occasionally parodied him, notably in the "Baby Fat" episode of The Dick Van Dyke Show.

[7][8] Martin appeared in all three of the classic Westerns released in 1969: Sam Peckinpah's The Wild Bunch (as Coffer, a bloodthirsty bounty hunter), George Roy Hill's Butch Cassidy and the Sundance Kid (as Percy Garris, the "colorful" Bolivian mine boss who hires the two title characters), and Henry Hathaway's True Grit (as Colonel Stonehill, a horse dealer).

Though he usually appeared in supporting roles, he had major parts in Hannie Caulder (1971), The Brotherhood of Satan (1971),[9] Pocket Money (1972) with Paul Newman and Lee Marvin, and in the horror film SSSSSSS (1973).

Martin later appeared in another George Roy Hill film, Slap Shot (1977), again with Paul Newman, as the cheap general manager of the Charlestown Chiefs hockey club.

In an interview originally published in Movietone News in 1981, Martin commented on his professional relationship with both Wayne and Newman: [Paul] never says so, but he cast me in Butch Cassidy.

In one of the skits, Martin played the strict owner of a French language camp for children, based on his role as the prison captain from Cool Hand Luke.