I’ve watched every episode of Trek, to save you from having to do so. No one needs to watch all of the episodes of TOS. In fact, most of Season 3 can be safely skipped. If you’re a Cliffs Notes type of person and just want to get the essence of the series, I’d recommend watching these ten episodes.
“The City on the Edge of Forever” — The original Harlan Ellison teleplay won a Hugo Award. The finished product wasn’t bad either. A time travel episode featuring the iconic line of dialogue: “Edith Keeler must die.” This is my favorite episode of Trek, period.
“The Menagerie, Parts 1 & 2” — I’m counting this as a single episode even though it’s usually shown as two. This episode includes the original pilot episode with Captain Christopher Pike. But the wraparound TOS story used as a framing device is also well-done. This one was going to be on the list even before Anson Mount showed up as Capt. Pike on Star Trek: Discovery.
“Space Seed” — Ricard Montalban chewing up the scenery and showing off his pecs. This deserved to be made into a feature-length Trek movie.
“Mirror Mirror” — This is the one that introduced the Mirror Universe and the Terran Empire, which continued to be a thing through all of the series including the current one.
“Balance of Terror” — This featured a tense submarine warfare sequence between Kirk and the Romulan Commander, played by future-Sarek, actor Mark Lenard. The unnamed Romulan Commander (who is often called “Keras,” which is “Sarek” spelled backwards) revealed that Star Trek enemies can display honor as well.
“The Galileo Seven” — This season-one episode demonstrates a lot of character growth in Spock, who is, of course, our favorite character from the original series. In this story, he shows true leadership in the face of adversity. And, we get our first close look at a shuttle, which will become a Trek staple.
“Amok Time” — Pon’farr, and Vulcan, and a Kirk and Spock battle to the death. For Vulcans, apparently, killing your best friend is the equivalent to a human cold shower.
“The Trouble with Tribbles” — A genuinely funny episode that also has a high stakes exciting story at its heart.
“Patterns of Force” — Everyone who knows me knows I hate Nazi Trek episodes. Except for this one: the first. McCoy especially makes a convincing Nazi.
“Journey to Babel” — The first appearance of Sarek, as played by Mark Lenard, and the antennaed, blue-skinned Andorians. It establishes the father-son dynamic between Sarek and Spock that continues even to present-day Star Trek. Plus, it includes a gripping central mystery.
Your mileage may vary in choosing your Essential Trek episodes, of course. For me, only the last two involved any internal debate; the first eight were a lock. It is no accident that none of these came from the final season.