In 1951, a 14-year-old Australian boy fell gravely ill and underwent surgery to remove three-quarters of his left lung. A transfusion of 13 units of blood saved his life. “I was a sickly child,” James Harrison says. “My life was saved by somebody I never knew. So why not return the favor?”

That is what he’s done for the past 60 years. As soon as he turned 18, Harrison began donating blood. Now 78, the retired railway administrator in New South Wales, Australia, holds the Guinness World Record as the most prolific blood donor....