- Drowned while filming a TV scene in Peru at age 41.
- During Fleming's enlistment in the Seabees in 1942, his face was shattered when a 200-pound block of steel slipped from a hoist. A long convalescence and four plastic surgical procedures created the face familiar to Rawhide (1959) viewers.
- Fleming was unmarried and had no children. He was to have married long-time companion Lynne Garber within two days of his death.
- He drowned while filming a movie in Peru. In his will, he donated his body and his eyes to the medical center at the University of California at Los Angeles. But after his body spent three days in the river his eyes could not be used in research.
- His last completed movie role was The Glass Bottom Boat, in which he uncharacteristically engaged in pratfalls with leading lady Doris Day.
- His mother's maiden name was Anderson.
- He relaxed by playing chess and bridge, sculpting and reading.
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