First, lemme single out one that hasn't been mentioned and that has great significance to the times we're living in:
Let That Be Your Last Battlefield deals with the destructiveness and stupidity of racism and bigotry. Here is the dialogue from the best scene, which features the brilliant Frank Gorshin:
Bele: It is obvious to the most simpleminded that Lokai is of an inferior breed.
Spock: The obvious visual evidence, Commissioner, is that he is of the same breed as yourself
Bele: Are you blind, Commander Spock? Well, look at me. Look at me!
Kirk: You're black on one side and white on the other.
Bele: I am black on the right side.
Kirk: I fail to see the significant difference.
Bele: Lokai is white on the right side. All of his people are white on the right side.
Kirk and Spock both look at each other in disbelief and exasperation....
Many of my favs have already been listed, so I'll lump them into a list of no particular preference
Balance of Terror - this is probably my favorite to rewatch
City on the Edge of Forever
Trouble with Tribbles
Journey to Babel
Devil in the Dark
Taste of Armageddon