TOS - "The Man Trap"

This is a great episode. It's a genuinely suspenseful story that surpasses the show's limited budget as well as the technological limitations of the time.

In this episode we really get a sense of the crew's comfortableness with each other. They really do seem like a family rather than a group of co-workers, as The Next Generation would do later.

On that note, however, an early scene in this episode has Uhura openly flirting with Spock, and attempting to get him to flirt back. I'm not sure if she was sarcastically mocking his emotionless manner or seriously trying to start up a relationship with her commanding officer. Either way, the scene was a bit uncomfortable. However, it did a very good job of establishing the fact that Spock has literally no interest in women.

One thing that bothers me about many of the TOS episodes is that many of the plots involve family or close friends of the bridge crew. It seems more than a little unlikely that Kirk, Spock, and McCoy would encounter close personal friends and family so frequently on their mission to uncharted space. However, that does not diminish the dramatic power of this individual episode, as McCoy is forced to "kill" his former lover.
Something that is notable about the "villain" in this episode is that it is no mere monster; the creature from M113 is an intelligent being, yet is also lonely and psychotic, being the last of its kind. Although pained by constant hunger, the creature can, in fact, suppress its hunger if it is given the love and attention is so desperately wants.
At the same time, it is a salt-sucking alien vampire, which is awesome.

"The Man Trap" is genuinely captivating the whole way through. This is undoubtedly one of the must-see classic episodes of Star Trek.