When Danny Thomas, the well-loved entertainer and benefactor of St. Jude's hospital for children, cast Andy Griffith as the affable slow-talking sheriff in an episode of The Danny Thomas Show (1953-65), he had no way of knowing that he was launching a phenomenon that would assume mythical proportions. In that episode, Thomas was given a ticket while traveling through the small town of Mayberry, North Carolina. Sheriff Andy Taylor, who also happened to be the justice of the peace, convinced the big city entertainer that Mayberry was a place to be reckoned with. Almost 40 years later, it still is. The show ran from 1960 to 1968, but by the end of the 1990s, more than five million people a day continued to watch The Andy Griffith Show in reruns on 120 television stations.

The genius of The Andy Griffith Show evolved from its characters. Each...