A long time ago I composed my own “essential TOS” list for my son who was watching DS9. A bit of a long post, but here it is (the third season picks are provisional and may change once my current rewatch gets up to there). I’m mildly surprised I have fully 34 picks.
TOS Season Zero:
(1) “The Cage” - the originally un-broadcast first pilot with an (almost) entirely different cast. A classic piece of 1960’s television and the foundation of Star Trek.
TOS Season One:
(2) “Where No Man Has Gone Before” - the second pilot which got the series on the air. Features Gary Lockwood of later 2001: A Space Odyssey fame, and the first appearance of Captain Kirk.
(3) “The Corbomite Maneuver” - perhaps the first episode featuring Roddenberry’s philosophy of the ability of mankind to rise above his baser instincts. Also, a very good episode.
(4) “The Naked Time” - the original. Accept no substitutes! Sulu as sword fighter!
(5) “Balance of Terror” - the first appearance of the Romulans, Mark Lenard, and cloaking technology. An excellent episode as well.
(6) “The Conscience of the King” - Star Trek does Shakespeare, with Kirk as Hamlet.
(7) “The Galileo Seven” - first appearance of shuttlecraft and a character study of Spock in command (spoiler: he’s not that great at it).
(8) “The Menagerie" - the only two-parter of the original series, written around the first pilot episode. Perhaps the greatest “clip show” in television history.
(9) “Arena” - the first and only appearance of the Gorn in the original series, featuring the famous Vasquez Rocks near Los Angeles. Pop culture touchstone.
(10) “Tomorrow is Yesterday” - not a great episode but it marks the first time-travel episode (with the minor exception of The Naked Time) in Star Trek and the first use of the stellar slingshot method of time travel (invented by Spock and Scott).
(11) “Space Seed” - Khan Noonien Singh! What more do we need to say? Ricardo Montalban’s greatest television role and Kirk’s greatest foe.
(12) “The Devil in the Dark” - we meet the Horta (okay, it is a lousy costume, but whatever). A classic episode about fear of the unknown and putting yourself in someone else’s shoes.
(13) “Errand of Mercy” - first appearance of the Klingons, who don’t waste time getting down to war right away. Features John Colicos as the first ever Klingon. Except they don’t look like Klingons.
(14) “The City on the Edge of Forever” - widely considered to be the greatest episode of the original series, in spite of the fact that it is a time-travel episode.
TOS Season Two:
(15) “Metamorphosis” - the first appearance in Star Trek of Zefram Cochrane, human inventor of the warp drive. Perhaps overly sentimental but I appreciate it more than when I was younger.
(16) “Who Mourns For Adonais?” - perhaps the most anti-religious hour of television ever to make it onto American prime time television in the 1960s? Not a fantastic episode, and it sort of pulled its punches at one point, but I’m surprised this got on the air in the USA.
(17) “Amok Time” - the classic episode that takes us to Vulcan for the only time in TOS. The “battle music” in this episode has been parodied everywhere in pop culture.
(18) “The Doomsday Machine” - a retelling of the Moby Dick story, featuring an excellent performance by William Windon as Commodore Decker of the USS Constellation.
(19) “Mirror, Mirror” - evil Spock with a beard! This episode has permeated pop culture as the archetype of the “evil alternative universe” trope. I think evil Sulu was a particular standout and felt he got more character development in one episode than good Sulu did in the entire series.
(20) “The Trouble with Tribbles” - a tale about what happens when you destabilize ecologies with invasive species, however cute and cuddly. The beginning of writer David Gerrold’s longtime involvement with Star Trek. More Klingons.
(21) “Journey to Babel” - where we meet Spock’s mother and father for the first time. We finally get to see other Federation races such as the Andorians and the Tellarites, plus the evil Orions put in an appearance.
(22) “A Piece of the Action” - this is one of the few outright comedy episodes of Star Trek. Although one of the this-planet-evolved-exactly-like-Earth-almost episodes that TOS abused way too often (I generally banish those from my essential TOS list), this one has an almost plausible explanation. And seeing Spock as a 1930s Chicago gangster should not be missed.
(23) “The Ultimate Computer” - the first and only appearance of Richard Daystrom, this is a fairly conventional episode about the fear of computers taking over your job. Daystrom’s name lives on in Star Trek all the way up to Star Trek Into Darkness. I thought that William Marshall’s depiction of a neurotic genius on the edge of breakdown was very striking. Starfleet really shouldn’t let those sorts of crazies install stuff into their ships.
(24) “Assignment: Earth” - the final episode of season two, this one is rather strange. Another TOS time travel episode where they go back to 1960’s Earth (again), but this time on purpose. This episode had been intended by Roddenberry to be recut (taking out the ST parts) as a potential pilot for a new TV series (that never happened). After all, Star Trek had nearly been cancelled twice, so it made sense to look towards something else. The resulting episode is a bit disjointed and weird, but one has to wonder how that new TV series would have fared if it had gone ahead.
TOS Season Three:
(25) “Spectre of the Gun” - a somewhat psychedelic homage to old TV westerns with atmosphere and striking set design. I hate westerns mostly, but I like this.
(26) “The Enterprise Incident” - another important Spock and Romulan episode. Torn from the headlines (USS Pueblo incident) in 1968.
(27) “Is There in Truth no Beauty?” - perhaps also not one that makes many people’s best-of lists, but it seems to fall for me in the same general category as does “The Conscience of the King” and “Metamorphosis”. I quite liked the performance of Diana Muldaur as Dr. Miranda Jones. Ms Muldaur always plays a doctor in Star Trek!
(28) “The Tholian Web” - first appearance of the Tholians as a very alien species. The only time we see the Enterprise crew wearing space suits in TOS. We’ll see the Tholians again (as well as the USS Defiant) in later Star Trek.
(29) “Spock’s Brain” - although an episode that is often derided (and I have to admit the brain-stealing part of the plot is not that great), it is an example of a more traditional science-fiction premise that I think kind of works.
(30) “For the World is Hollow and I have Touched the Sky” - another nice science fiction premise and a big episode for Dr. McCoy.
(31) “Wink of an Eye” - technically doesn’t quite work since the various “time-lines” don’t match up but it is a fun episode and a nice performance by Kathie Browne as Deela.
(32) “Whom Gods Destroy” - I think I must like episodes where we see at least a couple of different aliens, this time a pretty taciturn Andorian and (for the first time since the original pilot episode) another green-skinned Orion lady.
(33) “Requiem for Methuselah” - another of the drawing-room dramas that for some reason appeal to me in TOS, written by the great writer Jerome Bixby (see his great little film “Man from Earth” which shares a lot of its DNA with this episode).
(34) “The Savage Curtain” - I mean, Abraham Lincoln, what can you say? We also meet Surak, a Vulcan’s Vulcan, and some weird rock monsters.