Star Trek The Paradise Syndrome
Episode 57 - Elaan of Troyius - Kirk and the U.S.S. Enterprise are assigned to deliver Elaan, the beautiful Dohlman of Elas, to her rival planet Troyius. But her unruly behavior threatens to cost Kirk his ship. Episode 58 - The Paradise Syndrome - The Enterprise's mission: to deflect an asteroid from colliding with a planet. But shortly after Kirk, Spock and McCoy beam down to survey the planet, Kirk vanishes.
Episode 58 original airdate October 4, 1968. This video produced in 1987.
An episode with Romulan's and an episode where Kirk gets Married.