#4: Balance of Terror
In case you forgot: Federation colonies along OMG THE NEUTRAL ZONE have been attacked by Romulans. Kirk gives chase and ultimately destroys the ship. There's also some irrelevant nonsense about a wedding and some slightly less irrelevant nonsense about space racism.
It's the Romulans! And oh snap, they sure do look a lot like Vulcans. There must have been some level of shock and excitement at the reveal back when the episode first aired, because the mythos of TOS had yet to be established. As far as the audience knew, Spock really could be a Romulan spy. It's hard for viewers today to experience that same visceral shock—everyone knows Spock is a good guy—but the idea is cool enough that I'll still count it as a point in favor. We also have the first appearance of Mark Lenard, aka Sarek, as the Romulan commander. He is one of the highlights of the episode, and though he is totally a scumbag for destroying Federation colonies without provocation, you still feel bad when he opts to go down with his ship.
Again, like "The Corbomite Maneuver," this is an episode for Kirk to be an awesome captain of a starship, not a bull-headed Casanova who gets involved with planetary intrigue. Episodes that rely on the Enterprise being under the threat of death and destruction for the dramatic weight aren't as fun to watch, for me (of course they're going to survive!); episodes where you wonder how they're going to escape, rather than if they're going to escape, are where it's at. "Balance of Terror" is a great example of that.
Sometimes TOS forgets that it's in space, and that it can maneuver in all three dimensions. Surely the Enterprise could have switched to a course perpendicular to the trajectory of the Romulans' super plasma beam? An understandable mistake since the episode was inspired by submarine movies, I guess, but a little throwaway line about how the plasma beam is heat-seeking or locked on to the Enterprise or whatever would have been enough.
Why the wedding? Why? It's not like this episode needed any padding. At least the space racism with Stiles and Spock serves some sort of moralizing, Aesop-y purpose.