Simon was born in 1908 in Mansfield, Ohio, where he was an all-state high school basketball champion in the 1920s. He became an understudy to Lee J. Cobb for the lead in Arthur Miller's Death of a Salesman.
1950s–1970s
Simon appeared on Broadway in Clifford Odets's play, Clash by Night. In 1949, he succeeded Lee J. Cobb as Willy Loman in Death of a Salesman. In 1955, he appeared on television in episodes of Medic and Alfred Hitchcock Presents as well as such feature films as , , and The Court-Martial of Billy Mitchell. Actress Elizabeth Montgomery, who would later play Simon's daughter-in-law, Samantha, on Bewitched, made her film debut in The Court-Martial of Billy Mitchell. In 1956 and 1957, he appeared in episodes of State Trooper, The Millionaire and M Squad. In 1957, he appeared in the Betty Hutton film Spring Reunion, and as George Nordmann in the feature filmEdge of the City, starring John Cassavetes and Sidney Poitier. In 1958, Simon guest-starred as Captain Woods in "The Coward of Fort Bennett" on General Electric Theater. In 1957 and 1958, he appeared in four episodes of the anthology series, Playhouse 90. In 1959, he appeared on Peter Gunn and Adventures in Paradise. His other 1950s film credits included appearances in The Buccaneer, Compulsion, The Last Angry Man and Operation Petticoat.
Westerns
There were few television westerns in which Simon did not guest star. From 1956 to 1970, he appeared in Broken Arrow, Disneyland, Dick Powell's Zane Grey Theater, Laramie, Black Saddle, Law of the Plainsman, Johnny Ringo, Cheyenne, and The Dakotas, Wichita Town, The Man From Blackhawk, The Texan, Tombstone Territory, Tate, and Shotgun Slade, Stagecoach West, Bat Masterson, Lawman, Klondike, and Frontier Circus, Have Gun - Will Travel, Wagon Train, The Legend of Jesse James, The Road West, Gunsmoke, Laredo, The Virginian, Bonanza, and The Guns of Will Sonnett. In 1962, Simon played the part of Mackie in the episode "House of the Hunter" on CBS's Rawhide. The same year he also portrayed Handy Strong in the feature film The Man Who Shot Liberty Valance.
Drama
Simon appeared in such programs as Crusader, Route 66, Dante, The DuPont Show with June Allyson, Johnny Midnight, Straightaway, The Roaring 20s, Sea Hunt and State Trooper. In 1961 and 1962, he guest starred on episodes of Ripcord, The Dick Powell Show, The Lloyd Bridges Show, Cain's Hundred, The Defenders and Sam Benedict. Simon guest-starred three times on Perry Mason, including the role of murderer Edward Bannister in the 1958 episode, "The Case of the Desperate Daughter." Simon appeared as Harvey, friend of the main character Paul Driscoll in the 1963 The Twilight Zone episode "No Time Like the Past". In 1965, he appeared in episodes of Slattery's People, Voyage to the Bottom of the Sea, and Dr. Kildare. During the 1960s, Simon performed as well in dramatic roles in several films, such as The Spiral Road, Captain Newman, M.D., and Fate Is the Hunter. In 1966, he starred too as Mr. Rellik in the Highway Safety Films' production The Third Killer. His role was that of a "Death" salesman charged with three accounts, including traffic fatalities.
Comedy
In addition to Bewitched and Nancy, Simon appeared in other sitcoms, such as McHale's Navy, Mrs. G. Goes to College, Get Smart, and The Andy Griffith Show. He appeared in A New Kind of Love starring Paul Newman and Joanne Woodward, as "Cervantes" in The Reluctant Astronaut, and as a doctor in Private Duty Nurses. He appeared in a 1970 episode of Love, American Style, in a 1971 episode of Nichols, starring James Garner, and a 1973 episode of The Partridge Family. In 1973, he made three guest appearances as General Maynard M. Mitchell on M*A*S*H.
Later roles
From 1969 to 1985, Simon appeared in Marcus Welby, M.D., The Mod Squad, The Interns, Barnaby Jones, Hawaii Five-O, Cannon, Ellery Queen, Columbo, McCloud, Quincy M.E., Eight Is Enough, and The Feather and Father Gang. His last television appearance was in a 1985 episode of Airwolf.