Amok Time by Theodore Sturgeon
What a way to open season 2! Spock is not acting normally. He's not eating and he's grumpy. He requests leave on his home planet, Vulcan. McCoy discovers that if he doesn't get there and do whatever, he'll die from the overload of adrenalin. Kirk diverts to Vulcan in defiance of orders. Spock's fiancée, T'Pring, chooses the challenge over the marriage and then chooses Kirk as her champion. McCoy slips Kirk a mickey disguised as something to help him combat the heat and thin air. Spock "kills" Kirk, then finds him alive when he gets back to the ship.
Wow wow wow. So very much lore is established here. We see Vulcan for the only time in TOS. We learn Spock has been betrothed since he was seven. We learn about pon farr. We meet T'Pau - "All of Vulcan in one package."
We get fun Vulcan weapons. This is the first time we see the Vulcan salute and hear "Live long and prosper." Spock admits that Kirk and McCoy are his friends.
Beyond all that, it's a riveting episode. I've seen it a million times and I was still on the edge of my seat. Nimoy is superb here, showing how close to the edge he is in a million little ways. We also get THAT scene with Chapel and Spock, which has more resonance after SNW. Even if it's a little tough to reconcile SNW Chapel with TOS Chapel, when Spock wipes away her tear and calls her Christine, I could feel my heart skip a beat.
And T'Pring! Yes, it's a little hard to believe that the woman we met in SNW becomes this woman, but not impossible. As she says, "as the years went by, I came to know that I did not want to be the consort of a legend." Plus, there's Stonn. It makes sense she wanted out of the marriage and did the only thing that would let her out.
Plus, as Wikipedia notes, the music for the fight became a standard underscore for combat scenes in season 2. I'll be in the nursing home, having forgotten my own name, and still be able to place that music.
All in all, one of my Top 10 TOS episodes.