A former child actor, Dobkin began working in radio to pay for his studies at the Yale University School of Drama. He understudied on Broadway before serving with a radio propaganda unit of the United States Army Air Corps during World War II. When he returned to network radio he was one of five actors who played the detective Ellery Queen in The Adventures of Ellery Queen. In The New Adventures of Nero Wolfe (1950–1951), Dobkin played detective Archie Goodwin opposite Sydney Greenstreet’s Nero Wolfe. While playing Louie, The Saint’s cab-driving sidekick on NBC Radio in 1951, he was asked to step into the lead role of Simon Templar to replace Tom Conway for a single episode — making Dobkin one of the few actors to portray Leslie Charteris’ literary creation. His other radio work included Escape (1947–1954), Gunsmoke (1952–1961), Yours Truly, Johnny Dollar (1956–1960), and the anthology series Lux Radio Theater. “The few of us who are left,” Dobkin said of his radio days not long before he died, “keep telling each other that we never had it so good.” He was also Lieutenant Matthews on The Adventures of Philip Marlowe, along with several other characters. Continuing to work as a voice actor throughout his career, Dobkin contributed to the video game Tom Clancy’s Rainbow Six: Rogue Spear (1999). Dobkin began a prolific career in television in 1946, having worked as an actor, narrator and director. In 1953, he guest starred on Alan Hale, Jr.’s short-lived CBS espionage series set in the Cold War, Biff Baker, U.S.A.. He was cast in an episode of the early syndicated series The Silent Service, based on true stories of the submarine section of the United States Navy. He appeared too in the religion anthology series, Crossroads, based on experiences of American clergymen, and later on the ABC religion drama, Going My Way, starring Gene Kelly.

In the 1957-1958 television season, Dobkin played a director on the CBS sitcom, Mr. Adams and Eve, starring Howard Duff and Ida Lupino as fictitious married actors residing in Beverly Hills, California. He guest starred in 1958 in the first season of ABC’s The Donna Reed Show. In 1960, Dobkin appeared as Kurt Reynolds in “So Dim the Light” of the CBS anthology series, The DuPont Show with June Allyson and also as an escape artist on the run from a possible murder charge in Wanted: Dead or Alive. He also appeared in the David Janssen crime drama series, Richard Diamond, Private Detective. Dobkin also starred in a heartfelt episode of The Rifleman portraying General Philip Sheridan from the American Civil War. Often otherwise cast as the villain, Dobkin portrayed gangster Dutch Schultz on ABC’s The Untouchables. He appeared on the ABC/Warner Brothers crime drama, The Roaring 20s and in the NBC western with a modern setting, Empire. He was cast as a mass murderer in the 1972 pilot for ABC’s The Streets of San Francisco, starring Karl Malden. He guest starred on ABC’s The Big Valley, starring Barbara Stanwyck. He received an Emmy Award nomination for Outstanding Performance by an Actor in a Supporting Role in a Drama for his work in the CBS Playhouse program, “Do Not Go Gentle Into That Good Night” (1967). In 1991, Dobkin appeared on an episode of the television series Night Court as State Supreme Court Justice Welch. As a writer, Dobkin created the title character for the 1974 film and the 1977–1978 NBC series The Life and Times of Grizzly Adams. He began directing for television in 1960, and his work in this area included the pilot and episodes of The Munsters (1964), 16 episodes of The Waltons (1972–1981), and an episode of Sara (1976). Dobkin also appeared in several episodes of I Love Lucy: (“Equal Rights” and “Paris at Last”.)

Dobkin’s notable supporting film roles include Twelve O’Clock High (1949), The Day the Earth Stood Still (1951), Julius Caesar (1953), The Ten Commandments (1956), The Defiant Ones (1958) and Patton (1970). He had a cameo appearance in the 1954 sci-fi thriller Them. In an uncredited performance in Alfred Hitchcock’s North by Northwest, Dobkin has a memorable line as an intelligence official who remarks on the plight of the hapless protagonist, on the run for murder after being mistaken for a person who doesn’t exist: “It’s so horribly sad. Why is it I feel like laughing?”