In 1951, Burke played a jockey in the early television series Martin Kane. From then until 1980, he would appear in episodes of 103 different television series, as well as three made-for-television movies. Though never a series regular, he often played different roles in multiple episodes of the same shows. In 1959–60, he appeared five times as Tim Potter in the ABC western series Black Saddle starring Peter Breck. That same season, he appeared on Andrew Duggan's Bourbon Street Beat and John Cassavetes's Johnny Staccato detective series. He portrayed defendant Freddie Green in CBS's Perry Mason in the 1959 episode, "The Case of the Jaded Joker," the first of five appearances in diverse roles. In 1960 he played prosecutor James Blackburn in "The Case of the Ominous Outcast." Among his other roles he played a panhandler and a private detective. He guest starred as Hatfield in the 1961 episode "The Drought" of the syndicated western series Two Faces West. In the 1962–1963 season, he appeared on the CBS anthology series The Lloyd Bridges Show. In the 1965–1966 season, Burke appeared on another ABC western, The Legend of Jesse James. Burke played a Magician called "Zeno the Great" in a 1965 (first season) episode of Bewitched entitled "It's Magic". Burke also appeared on an episode of Lost in Space, playing Mr. O.M. in "The Toymaker" (1967). He also appeared in an episode of "Wild Wild West" as the mayor of a town under siege, in Hogan's Heroes as the master safe cracker Alfie the Artiste, and in two episodes of "Bonanza", as Jesse in "Destiny's Child" and as an unsuspecting witness in a trial.
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