Season two kicks off with an episode that can best be described as, well, fun. Spock finds himself at the mercy of the Pon Farr, the intense Vulcan mating cycle that clouds his logic and causes him to lose control of his emotions, eventually requiring him to return home and take a wife. Failure to do so would cause a chemical imbalance that could kill him. Interestingly, Spock is completely non-forthcoming about this problem—it's such an illogical and shameful dilemma that Vulcans cannot bring themselves to openly discuss.
"Amok Time" is the type of episode that is a success of attitude and character, and came at a time during the series where the characters were well defined. The plot isn't much to speak of, but it serves its purpose—although the rules of Spock's chemical-emotional overload seem a little bit arbitrary. (How could he be distracted by Kirk's death enough to overcome unconditional biological functions?)
A visit to Vulcan, a big fight between Kirk and Spock, and McCoy rigging the game with a clever ploy—it's irresistible stuff. And who could forget the classic moment when Spock finds himself overjoyed to realize that he hadn't actually killed Kirk as he had thought?