4. The Corbomite Maneuver
Early in the first season the crew of the Enterprise encounters a space buoy, and they destroy it. As the Enterprise continues on they encounters a massive starship called the Fesarius. Its commander, Balok, perceives the Enterprise as hostile and tows the Enterprise away to be destroyed. In this episode we see the development of Kirks character as a commander of a starship, his reliance on Spocks logic to help him make life or death decisions, and his friendship with McCoy, who appeals to Kirks compassion and humanity. The Corbomite Maneuver concludes with the Enterprise getting the upper hand in its conflict with the alien Balok, but instead of destroying Baloks ship, Kirk reaches out a hand in friendship. The human capacity for compassion is portrayed in many episodes (including Space Seed). The desire to put conflicts aside and foster peace and friendship is not only a hallmark of Star Trek but a bold vision for the future.
Memorable line: What am I, a doctor or a moon shuttle conductor? - McCoy