In 1943, Thompson, known for his boy-next-door good looks, was signed by Universal Pictures. He played quiet, thoughtful teens in Universal's feature films, including a lead opposite singing star Gloria Jean in Reckless Age, earning $350 weekly. During 1946, Universal discharged most of its contract players; that same year, Thompson moved to MGM and his film roles steadily increased and improved with appearances in The Clock and the lead in Gallant Bess, MGM's first film in Cinecolor.
Thompson married Barbara Long in 1949, making him a brother-in-law of actor Richard Long, best known for his role as Jarrod Barkley in ABC's The Big Valley. Thompson appeared together with his brother-in-law in the 1955 film Cult of the Cobra.
Thompson became a freelance actor in the 1950s and worked for various studios on a variety of pictures, including a number of horror and science-fiction feature films; this included the role of Carruthers in It! The Terror from Beyond Space (1958), one of the two films that would later inspire the plot for Director Ridley Scott's 1979 big budget feature Alien. Thompson also starred in the short-lived (13-episodes) 1959 syndicated science fiction TV series World of Giants. The drama follows Mel Hunter, a U. S. counter-espionage agent, accidentally miniaturized to just six inches in height, who must live in a dollhouse when not on missions.
He also guest starred as Arthur Poe in the 1960 Perry Mason episode "The Case of the Wayward Wife."
In 1965 he returned to MGM for the lead in the comedy-adventure film Clarence, the Cross-Eyed Lion (1965), in which he played Dr. Marsh Tracy, a Veterinarian and single father, raising his daughter (played by animal whisperer and Golden Globe winning Cheryl Miller) alone in Kenya. The film was then spun off into Daktari (1966–1969), a television series in which Thompson played the same role. Though the series was shot in California and Africa, Thompson and his wife made several trips to various African nations to film second unit footage that was then used in the series and in the film The Mighty Jungle (1965).
Thompson also was the host and storyteller for the TV anthology series Jambo (1969-1971).
Later in his career, he appeared in many television episodes and in feature films such as The Turning Point (1977) and The Formula (1980).
Thompson died in 1992 from congestive heart failure at age 66 in Royal Oak, Michigan. He was survived by his Barbara, their daughter and their grandson.