Here are my picks:
1. Mirror, Mirror (my personal favorite episode)
2. The Trouble With Tribbles
3. Amok Time
4. The Doomsday Machine
5. Obssesion
6. Tommorrow is Yesterday (watch it again, it's good)
7. Space Seed
8. Both Mudd episodes
9. The Tholian Web (rare show where Kirk isn't the center)
10. The Alternative Factor (ignore fans who call this stupid. They're wrong)
11. The Ultimate Computer
12. Metamorphosis (I usually hate "mostly planet" episodes, but this one's good)
13. The Enemy Within
14. The Rest of them.