The odds of a person encountering their doppelgänger are narrowing. Facial recognition software and the internet have made the identification of “double walkers” (from the German) into a pastime open to all amateur sleuths. But the thrill we feel today on spotting our likeness in others is a historic anomaly: Doppelgängers are more often associated with death than with pleasant diversion.

A slew of legends from across cultures cast them as paranormal duplicates and as phantoms to be avoided at all costs. From Queen Elizabeth I and Catherine the Great to the poet Percy Shelley—whose relatives claim he was greeted one night, shortly before his death, by a doppelgänger who asked him, “How long do you mean to be content?”—the apparition of a double has gone down in history a...