In broadcast order:
1. The Corbomite Maneuver
2. Balance of Terror
3. Mirror Mirror
4. The Doomsday Machine
5. Metamorphosis
6. The Immunity Syndrome
7. The Ultimate Computer
8. Assignment: Earth
9. Day of the Dove
10. The Tholian Web
That one with Kirk and he’s all, “Sulu......fire.....the phasers!”
That was one was cool.
1. The Menagerie
2. The City on the Edge of Forever
3. The Doomsday Machine
4. Amok Time
5. The Corbomite Maneuver
6. The Trouble with Tribbles
7. Mirror Mirror
8. Space Seed
9. Balance of Terror
10. The Devil in the Dark
1. The City on the Edge of Forever
2. The Naked Time
3. Where No Man Has Gone Before
4. Space Seed
5. The Galileo Seven
6. Arena
7. Shore Leave
8. The Doomsday Machine
9. This Side of Paradise
10. Journey to Babel
11. Mirror, Mirror
12. The Devil in the Dark
Balance of Terror
The Doomsday Machine
The Squire of Gothos
Nobody likes the one where Spock grabs Scotty by the collar and says, through gritted teeth, "I Don't Like That", after Scotty calls him "pointy-eared???
Memory Alpha.
The first season had a lot of good ones so I'll be creative and do a Top 15 based top 5 all three seasons with an honorable mention for each season:
Season One
1. Space Seed
2. The Enemy Within
3. The Galileo Seven
4. The Man Trap
5. The Devil in the Dark
Honorable Mention: This Side of Paradise/Where No Man has gone before (The latter was a pilot episode but was placed in Season One. If you want strictly season one then I included This Side of Paradise with those deadly spores and the beautiful Jill Ireland.)
Season Two
1. Who Mourns for Adonais?
2. Mirror Mirror
3. The Doomsday Machine
4. Catspaw
5. By Any Other Name
Honorable Mention: A Private Little War with the poisonous white ape.
Season Three
1. Day of the Dove
2. The Tholian Web
3. Whom Gods Destroy
4. Let That Be Your Last Battlefield
5. The Savage Curtain
Honorable Mention tie: That Which Survives/The Lights of Zetar, I liked both episodes equally so I included them here.