"I'm Captain Kirk!" So screams Kirk's "evil" doppelgänger, the result of (naturally) a transporter accident. Full of raw emotion, Kirk's double violently wreaks havoc (and an attempted rape!) while the good captain's more rational self struggles to solve a crisis involving crew members stranded on a freezing planet.
When Kirk realizes that half a man can't live, and he begs his friends to help him make a command decision which he lacks the faculty to, the Kirk-Spock-McCoy dynamic is forged. Spock, half-human, half-Vulcan, constantly at war with himself, offers a logic-based perspective to Kirk's dilemma, as McCoy passionately argues the other side of it -- with a literally torn Kirk caught in the middle. Many subsequent episodes would do their spin on having a double, but none have done it better than the original.