Born Raymond William Stacy Burr on May 21, 1917 in New Westminster, British Columbia, he spent most of his early life traveling. As a youngster, his father moved his family to China, where the elder Burr worked as a trade agent. When the family returned to Canada, Raymond's parents separated. He and his mother moved to Vallejo, California, where she raised him with the aid of her parents. As he got older, Burr began to take jobs to support his mother, younger sister and younger brother. He took jobs as a ranch hand in Roswell, New Mexico; as a deputy sheriff; a photo salesman; and even as a nightclub singer.

During World War II, he served in the United States Navy. In Okinawa, he was shot in the stomach and sent home. In 1946, Burr made his film debut inSan Quentin (1946). From there, he appeared in more than 90 films before landing the titular character onPerry Mason (1957), the role for which he was best-known. Decades later, he reprised the role opposite former co-star Barbara Hale in a series of NBC television movies. At age 65, he returned to teaching drama as a professor of theatre at Sonoma State University, Rohnert Park.

After a brave battle with cancer, Burr died at age 76 on September 12, 1993 at his ranch home in Geyserville, Sonoma County, California. Married once, the union ended in divorce. He had no children.