#26: Errand of Mercy
In case you forgot: The Enterprise's mission is to obtain permission from the residents of the planet of Organia to build a Starfleet base there, as it is a key strategic point for both the Federation and the Klingons. The Organians refuse and Kirk can't deal with it; the Klingons come and take over and Kirk can't deal with it; finally, the Organians (who are of the ~beings of pure energy~ variety, surprise!) stop all the fighting and tell the Klingons and the Enterprise both to basically "go, and sin no more."
Mostly I just really like the Organians. They are perfectly, incredibly mellow, even when dealing with Kirk and his temper tantrums. Often TOS encounters alien races who claim to despise violence and destruction, despite begetting more violence and destruction themselves (see last week's Metrons). The Organians, on the other hand, are consistently and totally pacifist. They stay out of the conflict until they absolutely have to, and they do it in a fairly minimal, noninvasive way, without killing anyone or destroying anything.
If the Aliens of the Week are cool, though, our Power Trio is carrying the idiot ball. Not once do Kirk and Spock stop to think that the Organians may have a reason for being so confident in their own safety. Understandable in Kirk's case—he seems pretty eager to phaser some Klingons, much as he may insist otherwise—but come on, Spock! If the Organians are ~beings of pure energy~, wouldn't he notice that they weren't really growing or consuming any food or resources in his little scientific survey? He managed to pick up on the fact that they were "totally stagnant," after all.
If the Organian's power is as immense as is implied, why haven't they stopped violent conflicts before? Why don't they just tell Kirk and Kor right off the bat, "We're beings of pure energy, it's impossible for you to hurt us and we won't let you hurt each other, GTFO."?