From television:
10. Chain of Command from TNG. (What
JirinPanthosa said.)
9. Space Seed from TOS. (Khan is an iconic villain for good reason.)
8. Mirror, Mirror from TOS. (Striking concept episode and one of TOS' best Bradburyesque stories.)
7. Best of Both Worlds from TNG. (What
HGAL said.)
6. City at the Edge of Forever from TOS. (A common number one and it is great.)
5. The Emissary from DS9. (What
HGAL said.)
4. Darmok from TNG. (Best first-contact episode in probably all of Trek.)
3. Duet from DS9. (Most dramatic punch ever packed by an episode of Trek, and the furthest it ever successfully reached outside its core format.)
2. The Doomsday Machine from TOS. (Classic SF Berseker-style storyline. Some of the best-balanced true SF and true action-adventure the show achieved.)
1. Balance of Terror from TOS. (Embodied TOS' distinctive aspirations to stealing the heck out of classic tales from other genres and making them even more awesome. It's arguably still unrivalled as the best space duel any of the shows ever featured.)
(Honorable mentions for
In the Pale Moonlight,
The Pegasus,
Yesterday's Enterprise,
Arena, and...
Masks. Yes, I said it.)
In film, TWOK is the apex of the film franchise period for me (an early success that, ironically,
overshadowed and stunted a lot of later efforts that tried to replicate its magic without fully understanding it). A good film period, not just a good Trek film.
TMP was a stronger outing, too, than it's usually given credit for, and it still has a lot of charm for me.