In 1980, Robbins appeared on the PBS music program "Austin City Limits" (season 5). In addition to his recordings and performances, Robbins was an avid race car driver, competing in 35 career NASCAR Grand National Series races with six top-10 finishes, including the 1973 Firecracker 400. In 1967, Robbins played himself in the car racing film "Hell on Wheels". Robbins was partial to Dodges prepared by NASCAR Hall-of-Famer Cotton Owens, and owned and raced Chargers and then a 1978 Dodge Magnum. He was also the driver of the 60th Indianapolis 500 Buick Century pace car in 1976. His last race was in a Junior Johnson-built 1982 Buick Regal in the Atlanta Journal 500 on November 7, 1982, a month before his death.