Balance of Terror SEASON 1, EPISODE 13
Wiki Entry:
http://en.wikipedia.org/wiki/Balance_of_Terror
Wow, this is a terrific episode. Never was Kirk cooler than in this one, I think, and he has a great adversary in Mark Leonard's Romulan Commander (Mark Leonard would pop up later in Trek as Spock's father, Sarek - and his work here shows he's an excellent actor for such a role). There's some filler in there about weddings and a couple, plus a little intra-bridge conflict between a guy who lost some of his ancestry to Romulans, who antagonises Spock, because Vulcans and Romulans look the same (which is rather good).
A great episode, with the writing making it very clear how the Captains are trying to outthink each other and work out how to succeed and handle the situation, and introducing the Romulans to us.
No red shirts down in this one, but let's just say the wedding is put off indefinitely by the end.
Running Red Shirt Dead Count: 2
Also, Yoeman Rand's last appearance (in production order).
Classics -
The Naked Time (S1E04)
The Corbomite Maneuver (S1E10)
Balance of Terror (S1E14)
The Enemy Within (S1E05)
Miri (S1E08)
Charlie X (S1E02)
Decent -
Mudds Women (S1E06)
The Menagerie (S1E11+12)
The Conscience of the King (S1E13)
Where No Man Has Gone Before (S1E03)
The Man Trap (S1E01)
What Are Little Girls Made Of (S1E07)
Dagger of the Mind (S1E09)