Arena
Yes, this is the one where Kirk fights a Gorn, otherwise known as one of Trek‘s least convincing aliens. “Arena” sees the Federation and the Gorn on the brink of war until the mysterious Metrons pluck the captain of each ship and force them to fight in combat in order to discern the winner of the conflict.
This fairly straightforward plot marks an important moment for Kirk’s character, though. He’d already proven himself to us as a hero while sitting in the captain’s seat on board the Enterprise, but this shows us that he can handle himself with just his own smarts, too, which he uses to outwit the Gorn. More importantly, he proves his compassion as well when he decides to defy the Metrons and refuses to kill his enemy.
“Arena” might not be the episode you’d show a non-fan to make them take Trek seriously, but if you get past the dodgy costuming, this is smart episode that looks at the wider world of warfare, and the merit of mercy, through the lens of a one-on-one fight.
Space Seed
“Space Seed” is otherwise known as the episode that introduces perhaps’ Trek‘s most infamous villain into the show’s mythology, the genetically-enhanced superhuman Khan Noonien Singh, as brilliantly played by Ricardo Montalban (sorry, Benedict Cumberbatch, you’re awesome, but you couldn’t top the original).
What’s great about Khan in his first appearance is how he’s portrayed as the anti-Kirk, someone who’s got an even bigger ego and eye for the ladies that Shatner’s captain. When the Enterprise comes across the SS Botany Bay drifting dormant in space, Kirk decides to wake up the crew, but this turns out to be a bad idea when he realizes Khan and his people are remnants from the Eugenics Wars of the 1990s (hey, that seemed a long time away back in the 60s).
The resolution of this episode sees Kirk offer his foe mercy, dropping the charges against the warlord as long as he settles peacefully on the planet Ceta Alpha V. It’s a move that he would come to regret, though, as Khan would of course return with a vengeance in Star Trek II: The Wrath of Khan.