"The Omega Glory." Honestly, the only genuinely bad episode on this list. "Catspaw", easily the next weakest show, is goofy, silly, but amusing campy fun, "The Apple" is pretty much the archetypal TOS episode - it's got a bevy of redshirts dying, Scotty doing magical repair work, Kirk destroying a computer god and initiating the 60s sexual revolution in the Garden of Eden, and Spock and McCoy bickering. Sometimes I think every cliche and preconception about the show came from this one episode.
Almost as influential, if only for its fight music, is "The Gamesters of Triskelion." And the idea of malevolent gamester brains is campily hilarious. I enjoyed "Who Mourns for Adonais?", one of the few god killing episodes when the crew kill a recognisable God. This is a pretty good entry.
And "I, Mudd" isn't just a genuinely good episode; it's the best comedy episode TOS did. Yes, it's funnier than "The Trouble With Tribbles." I said it, and I go now to my gallows for heresy, but it had to be said.

The dialogue is sharp and Roger C. Carmel is a blast.
"You see, gentlemen, behind every great man, there is a woman urging him on. And, so it was with my Stella. She urged me on into outer space– not that she meant to, actually, but with her confounded, continual, eternal nagging – I think of her constantly; and every time I do, I go further out into space."