katarik: what on earth are spock-hands?
Betty: You know, live-long-and-prosper hands.
Katarik: ???
Betty: ...wait, is Star Trek another-- OH MY GOD.
Betty: are you even FROM THIS PLANET?
Katarik: i've seen a couple episodes! honest! i saw one of the movies!
Katarik: this conversation makes merfilly say that i was decanted poorly prepped.

So, in honour of Katarik-is-from-another-planet-but-certainly-not-the-planet-Vulcan, and in honour of brain-eating Zombie-Spock, five episode guide to TOS (Also a five episode guide to K/S, but not my fault, TOS was just like that.)

In the order they aired (although TOS was not really the sort of show where that mattered a whole lot) synopses taken from Trek Nation. If you honestly have never seen TOS, just to get this out of the way: it was an earlier time; a more innocent time; a time of ... cheese. But if you can get past that, there's some good stuff. The episodes titles are linked to the full episode from CSB.com, which, if you are American (I'm not), you can supposedly watch.

Five Episodes:

The City on the Edge of Forever

Synopsis: "An accidental drug overdose sends Dr. McCoy on a disastrous trip through a time portal, where he changes the course of Earth's history. Kirk and Spock pursue him into the past, where Kirk falls in love with a social worker whose life plays a pivotal role in the events McCoy will affect."

The script was written by Harlan Ellison, but don't let that put you off it. It also contains proto-fangirl Edith Keeler who says Spock belongs "At [Kirk's] side, as if you've always been there and always will," and asks, "Why does Spock call you 'Captain'? ... Even when he doesn't say it, he does."

Amok Time

Synopsis: "Spock enters the pon farr, the Vulcan time of mating, and Kirk returns him to Vulcan against Starfleet orders. But when his bride chooses to challenge the arranged marriage, she chooses Kirk as her champion."

Responsible for a million pon farr fic, but also a worthwhile episode in its own right for the Kirk/Spock emooooooo-porn. Uh, I mean, insights into Vulcan sociology and biology. *looks shifty.*

Mirror, Mirror

Synopsis: "Four crewmembers switch places with their parallels in another universe, where savagery reigns and advancement is by assassination. While Spock quickly realizes the situation and takes the alternate Kirk, McCoy, Scotty and Uhura into custody, Kirk must first try to evade detection and then convince the alternate Spock of the logic of changing his universe."

Responsible for giving us the phrase spock-with-a-beard as shorthand for "wacky AU hijinx." What, that's just me? Okay, watch it because Evil!Spock is sort of hot, and Evil!Uhura and Not-Evil!Uhura are both hot, and Evil!Kirk is sort of... petulant. Spawned a million sketchy fic.

The Enterprise Incident

Synopsis: "When Kirk goes insane and orders the ship into Romulan space, Spock becomes very close with the Romulan Commander who tries to seduce him into working at her side. Unfortunately for her, Spock's more interested in the Romulan cloaking device."

Spoiler: Kirk's not really insane. Worth watching for Spock's sort of awkward, but a bit touching all the same, flirtations with the Romulan lady Commander, (Romulans were much better feminists than the Federation (see: Turnabout Intruder)) and the slightly recursive fakery with prosthetics.

Turnabout Intruder

Synopsis: "A jilted lover of Kirk's who has always wanted to command a starship forces him via an alien machine to switch bodies with her, trapping him in her dying form while she takes over the ship. But her behavior quickly causes suspicion, and Spock mind-melds with the woman to discover Kirk's consciousness within."

Partly worth watching for watching Shatner's acting skillz: his "I'm Janice Lester!" is a bit, um. But Sandra Smith, who plays Janice Lester and Kirk-In-Janice-Lester's-Body, really shines, and her contribution to the Kirk and Spock's relationship is quite fascinating. From a feminist perspective, worth watching for the line "Your world of starship captains doesn't admit women," the interpretation of which, while debated, was supposedly interpreted by Rodenbury as a straight-up accusation of sexism, which is a topic Trek otherwise preferred not to acknowledge.

Supplemental Material, did not make the cut:

Spock's Brain

Synopsis: "A group of women steal Spock's brain to run the computer which keeps them safe from the savage men who live outside their underground city."

Worth watching: Really not. Widely acknowledged to be the worst episode made, this one is cringingly bad and cheesetastic. Remote-control Spock is wildly un-erotic. Included in honour of brain-eating zombie-Spock.

The Gamesters of Triskelion

Synopsis: "Kirk, Uhura, and Chekov are dragged hundreds of light years away by the gambling leaders of the planet Triskelion, who force aliens to participate in combat to the death for their amusement. Kirk makes a bet with the aliens to win the freedom of all the thralls."

Included as an example of the way those original-trek writers were sort of perverts: Hey, let's put the cast in body-harnesses, oil 'em up, and make them fight! There can be scenes with floggings, and, oooh! Maybe some "arranged breeding." Classy! There's probably twenty episodes exactly like this.

The Trouble With Tribbles

Synopsis: "Adorable creatures which eat and reproduce constantly interfere with Kirk's assignment to protect a shipment of grain, but they save the day when it's discovered that tribbles don't like Klingons."

Just a fun episode. Notable because the script was submitted by fan David Gerrold, blurring the line between fanon and canon, but honestly, it's great fun to watch. One of the better-known episodes, and reveals that cats tribbles looooooove Spock. Also taught me everything I know about triticale. (Which, obviously, is not a lot.)

Feel free to contest my choices or offer your own five in the comments!