I don't really remember a lot of the episodes, but one that seems to stick in my mind is the one where Sulu gets trapped on that really cold planet and almost dies waiting for the crew to get him. For some reason, I always thought it was cool that he generated heat by using his phaser on a rock.
By the way, and I'm not kidding here, Spock is a blood relative of mine. Distant, but related. It's always hard to remember, but I think he's my second cousin, once removed.