So Space Seed, the episode which introduced Khan, is not on this list, although it is on every Trek top 10 list. I excluded it because I don’t feel it stands on its own. While it’s certainly good, it’s the follow-up movie 15 years later that makes it retroactively great. And even then, the emotional core of Wrath of Khan (and the rest of the film franchise) isn’t inspired by that episode – it’s inspired by this one.
I also think Amok Time inspired this line in Galaxy Quest:
Our goals, our values had become scattered. But since the transmission, we have modeled every aspect of our society from your example, and it has saved us. Your courage and teamwork, and friendship through adversity.
… plus this scene from Futurama:
The fight scene – friends forced to kill each other! – has been done and redone so much that it ranks as among the most iconic scenes in all of TV, not just sci fi.