These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Kirk and the Enterprise, the only lady he truly loves. Made hilarious by one episode in which the ship's computer is programmed to call him "dear".
Hell, in "Elaan of Troyius" Kirk is able to single-handedly overcome a love potion just because he loved the Enterprise so much!
"Don't you think you ought to...rephrase that?"
Crowning Moment of Heartwarming - In "Amok Time" after Spock had believed he had killed his captain and friend. He went to McCoy and began readying himself for court martial, but just as he began giving McCoy orders to turn the ship over to Scotty, Kirk walked in behind him, snarking, "Don't you think you'd better check with me first?" Spock grabbed his friend by the shoulders, whirled him around, let loose with a beaming smile and cried, "Jim!" At which point every viewer watching squeed. Oh for... Here. First minute or so.
Ensemble Darkhorse: Hikaru Sulu's popularity has gone way up in recent years, in no small part due to George Takei's newfound prominence as a civil rights activist. Having an insane number of followers on Facebook and Twitter doesn't hurt either.
Uhura: Although now it seems normal and unremarkable for a woman to have a job other than a secretary, back then Uhura being in a (almost military) job and being black was a huge leap forward.
Not only that, even when she primarily served as The Chick, casting a black woman in the role was a huge deal in the 1960s. And novels written as early as the '70s indicate that Uhura was far more than a glorified switchboard operator — she is in fact a linguistic genius who can leave Kirk's head spinning with language theory.
One story going around is that Uhura's actress was considering leaving the show at one point, but was called up by Martin Luther King, Jr. himself, who told her how much the world needed to see an African-American woman on television being treated as an equal by White characters.
Sulu: Not to the same degree as Uhura, but it does not seem particularly notable or progressive today to have an Asian supporting character while all the leads were white. However, in the 1960s, it was a pretty big deal that Sulu had no accent, did not do martial arts, and overall was not an offensive stereotype of Asians. Just about every Asian-American actor was clamoring for the role as a result.
Of course, martial arts did eventually creep into Sulu's character by the third movie, and one animated series episode has a slightly uncomfortable joke about Asian racial stereotypes.
And he was going to have a big martial arts scene in "The Gamesters of Triskelion" before Takei had to bow out of the episode, resulting in him being replaced with Chekov and the scene becoming a standard '60s TV fight.
While marred by the pop-culture idea that he's a playboy, the fact remains that even for today's standards, Kirk is one of the few male heroes who use the stereotypically feminine technique of using their sexuality to get information.
Confirmed by Peter David in his TNG novel Q Squared. Though, as it turns out, Trelane is actually Q's son. However, this also means that Kirk did technically meet Q, when Trelane's parents arrived to take him away.
The (technically) two seasons which compromise Star Trek The Animated Series are actually the fourth and fifth year of the five year mission mentioned in the opening credits. The animated series isn't a different show, but the same one. Except its a cartoon.
Evil Kirk's assault of Rand during "The Enemy Within" is pretty awful in light of the fact that Grace Lee Whitney was later sexually assaulted by one of the Trek producers.
In the episode "Assignment: Earth", Spock lists several scenarios that Gary Seven could have been sent to effect in 1968 Earth. One of them is "an important assassination". The episode aired March 28, 1968. Martin Luther King Jr. was assassinated on April 4, 1968. To twist the knife even further, Robert Kennedy's assassination occurred just two months later.
In the aftermath of incidents like the Manson murders, Dr. Sevrin's actions in "The Way To Eden" become a lot more disturbing.
The message in "A Taste of Armageddon", about the dehumanizing effects of computerized warfare, was haunting enough in 1967, when the computer was still in its infancy. Today, with things like UAVs and computer-guided missiles becoming indispensable parts of modern warfare, it hits harder than ever.
"The Menagerie" when you consider that Jeffery Hunter (Captain Pike) was later injured in an on set explosion on a film set that eventually caused him to be partially paralyzed and lose his power of speech. Eventually, he recovered but later still died from a cerebral hemorrhage caused by the explosion.
In "The Way to Eden" one of the female space hippies tries to seduce Sulu, who doesn't bite. And says "How do you know what I want?" with a giant grin on his face.
Ho Yay: Spock had so much of this with Captain Kirk that entire web shows and essays have been devoted to it, and it spawned Slash Fic as a genre. But his Slap-Slap-Kiss with Dr. McCoy shouldn't be ignored...
See the trope page itself for many, many more examples.
Iron Woobie - Spock is perfectly willing to sacrifice himself for others. He will also stand by his principles even when he expects that Kirk, McCoy, or his parents will hate him for it.
My Real Daddy: Gene Roddenberry was responsible for the series as a whole, but one of his producers/writers, Gene Coon, had a great deal to do with making the show great with classic ideas like the Klingons, the Prime Directive, Khan Noonien Singh and being the series' showrunner in the first two seasons who helped many of the stories used better.
Narm - Some aspects of the show have aged horribly, especially for people born after 1990; as a result, this trope ends up popping up in places where it's obvious that wasn't the intent at all. Of course, a lot of people don't see this as a bad thing, as noted directly below.
Once you're familiar with the concept of Redshirts, it's pretty hard to take their deaths seriously. Indeed, when you're thinking, "Yup, that guy's dead" as soon as they beam down, then when the time comes it can produce chuckles.
As the show went on, the missions just kept getting weirder and weirder. Prime examples include looking for Spock's brain, a showdown at the O.K. Corral and encounters with hippies, Chicago Gangsters, Native Americans, a modern day Roman Empire, Nazis, Abraham Lincoln and even the Greek god Apollo.
In fact, the episode "Spock's Brain" is usually regarded as the absolute worst episode in at least the original series and sometimes in the whole of Star Trek.
Given a Lampshade Hanging in some of Kirk's in-universe biographies, which typically note that many of Kirk's reports were met with considerable disbelief from his superiors in Starfleet. The case where an alien race literally stole Spock's brain is usually mentioned in an especially disdainful manner.
Seinfeld Is Unfunny - Fwoof. TOS catches it bad these days. Not only has everyone who followed in its footsteps borrowed from it to some degree, but they've all tried to improve upon a lot of the problems the show had due to a limited budget, technological barriers of the time and the fact that the cast and crew were inventing a lot of tropes as they went. Fans who got into Trek with the newer installments can have trouble watching TOS nowadays.
Stoic Woobie - Spock definitely falls into this category. He's an alien to two races, and several times he is injured in the line of duty, or stands by his principles under severe criticism. A few episodes that highlight this are Journey to Babel, Operation: Annihilate, and the Tholian Web.
They Changed It, Now It Sucks: For those who dislike the "remastered" episodes (and especially resent that CBS is obviously trying to supplant the original versions with them - though at least they aren't going full Lucas).
TOS features one of the few instances of the franchise boldly going into this territory, in "The Paradise Syndrome". Kirk loses his memory, goes native on the Planet Of The Week and falls for the Girl of the Week - in this case, the natives being translocated descendants of Native Americans. Yes, that's right, Trek featuring a "mighty white man conquering the beautiful, suggestible native woman" story. (The natives even straight-up mistake Kirk for a god. Yep.) It was barely acceptable when it aired, and these days is almost universally seen as an embarrassment and one of TOS' lowest points. (This was a third season episode, natch.)
Not to mention the show's open sexism. In one episode the effects of a Negative Space Wedgie causes members of the crew to start passing out, Kirk orders them given booster shots. McCoy is later shown injecting a line of Starfleet personnel — who are all female. Presumably tough spacemen are not in the habit of swooning. To the point of the Bridge Bunnies wearing incredibly short skirts and generally having menial, unimportant roles except as background characters or the Captain's Girl of the Week.
Although keep in mind that at the time, the miniskirt was a symbol of feminine empowerment. Yes, the short skirts were in the show as Fanservice, but that isn't the only purpose they served.
Another example was Wolf in the Fold, which involved the spirit of Jack the Ripper feeding on peoples' fear. How is that sexist? Because the spirit overwhelmingly preyed on women, and Spock explicitly stated that this was because women feel fear more strongly and easily than men. (If you look carefully, the female crewmember in the foreground looks distinctly unimpressed when the line is read...)
Perhaps the worst of all is "Turnabout Intruder," which reveals that Roddenberry's vision of an ideal, utopian future (and Roddenberry himself came up with this story, mind you) includes women being legally barred from becoming starship captains. This one was such an embarrassment to latter-day Trek that an episode of Enterprise casually revealed that Starfleet did allow women to be captains, implying that Janice Lester's psychotic mind imagined that bit of oppression.
Though it should be noted that Roddenberry was actually forced to put in the bit about women not being allowed to command starships and did not enjoy being forced to put it in.
In "The Return of the Archons" Kirk feels that the computer that has been running the society of Beta III is just a machine and has no soul, and that therefore there's no problem in destroying it. The crew of a certain otherEnterprise might have a thing or two to say about that.
In "The Changeling" there is a robot that looks very much like a Dalek that steal's Uhura's memory. The robot said that her thinking was irrational. Kirk replies, "That's a woman!" To make it even worse, when Uhura is being rehabilitated, she remembers how to speak Swahili. This have the implication that Swahili is very primitive compared to English.
Alternately, though, they may simply have been saying that Swahili is easier to learn than English (which isn't unreasonable, considering the high number of non-standard pronunciations in English), or they just thought it made sense that Uhura would remember how to speak her first language before remembering how to speak her second language.
Values Resonance: Several episodes, like "A Taste of Armageddon", and most notably, "Let That Be Your Last Battlefield".