Burton resided in California for 30 years. He attended Immanuel Baptist Church in Highland, California. He had two sons, one of whom, Martin, died of a heart attack at the age of 43 on May 8, 2014. He also had two daughters, Juanita and Christal. 
Burton was a talented chess player. Stanley Kubrick was defeated by him on the set of The Shining, in which Burton played Larry Durkin, the garage owner. Speaking with Kubrick biographer Vincent LoButto, Burton recalled his first day on the set: “My contract was for a week. I just had two short scenes in the movie. I stayed for six weeks because Stanley and I were playing chess… Stanley was a stronger player than I but I was strong enough to give him sufficient struggle to where he enjoyed it. I beat him in the first or second game we played, and then I didn’t win any more after that, but it was always a tight struggle. That’s what he loved; I guess there was no one else around that played strong”
