In 1971, Richard became a regular performer on Rowan & Martin's Laugh-In. After Laugh-In ended in 1973, Mark Goodson signed Richard to appear as a regular on Match Game '73. Dawson proved to be a solid gameplayer and was the frequent choice of contestants for the "Head-to-Head Match" portion of the show's bonus round.

In 1976, Richard got to host his own show, Family Feud. Unlike his flop in 1974 with Masquerade Party, Family Feud became a hit, soon surpassing Match Game '77. In 1978, he left the Match Game. After Dawson became a naturalized citizen of the United States in 1984, he showed his passport and photo during the introduction of an episode of Family Feud. He continued hosting the Feud until it was cancelled in 1985.

Dawson co-starred in the movie The Running Man in 1987, playing evil, egotistical, dark-sided game-show host Damon Killian. He hosted an unsold pilot for a revival of the classic game show You Bet Your Life in 1988. In 1994, Richard returned to Family Feud for one season. Dawson was considered for the current version of Family Feud, but elected not to host.

There was a rumor that spread claiming that Dawson had committed suicide after his return to Family Feud had failed. In actuality, it was Ray Combs, the man who replaced him (and whom he in turn replaced in 1994), who committed suicide (in 1996). Dawson currently resides in Beverly Hills, California with his wife since 1991, Gretchen (Johnson) Dawson, whom he met when she was a contestant on Family Feud. They have a daughter, Shannon Nicole and 3 grandchildren, Lindsay Dors Dawson, Tyler Emm Dawson and Emma Rose Dawson, all fathered by Gary.