Burkley was married to Laura Alderdice from 1967 until his death.
Although he had many acting credits, his most recognizable television roles include Cal, the Texas-born junkyard partner of Fred G. Sanford in Sanford, the short-lived Sanford and Son sequel from 1980-1981. He played a cannibal on an episode of Night Court. He appeared as Bubba in the TV series The Dukes of Hazzard in Season 2, Episode 18, called "Find Loretta Lynn". He provided the voice of several supporting characters on the animated television series King of the Hill (set in his home state of Texas). In 2005, he wrote and directed a film titled Repetition and also played a small role in the television series My Name Is Earl.
In films, he played Dozer, a biker with a severe speech impediment who befriends Rocky Dennis and his mother in the movie Mask. Burkley appeared in the drug culture drama Rush in 1991, the Chevy Chase comedy Fletch Lives, and Sylvester Stallone's Stop! Or My Mom Will Shoot. He appeared in the Kevin Costner golf comedy Tin Cup.
He died in his sleep of a heart attack in Los Angeles, California, on July 14, 2013.
