Anti-Hero: Sixties sex symbol or not, Kirk stumbled into Type I in The Wrath of Khan where his mid life crisis wears heavy and some poor choices cost the lives of many recruits (and a bulging waistline and receding hairline didn't do him any favors...) Type II in The Undiscovered Country and Star Trek 2009.
Companion Cube: Kirk's strongest love in the TV series is for the Enterprise herself; this may vary between Happily Married and The Masochism Tango. The movies have this become overshadowed by loyalty to his Nakama, culminating with his painful decision to self-destruct the original 1701 in Star Trek III.
Gunboat Diplomacy: One of his favorite diplomatic techniques seems to be threatening to blow up a planet that doesn't do what he wants. Somehow he gets away with this. He's Kirk.
Improbable Age: Minor example in-universe. Background material states that, at 30-ish, he is the youngest man yet to command a first-rate Starfleet ship.
Officer and a Gentleman: In addition to judo-throwing aliens and romancing Green Skinned Space Babes, he finds time to be well-versed in classical literature and offer aid to space-borne refugees.
Papa Wolf: Hurting his people causes him much Angst. And more anger.
Shirtless Scene: It's not quite to the level of Walking Shirtless Scene, but Kirk appears shirtless a lot in the original TV show. Mostly famously, it's caused by Clothing Damage during action sequences, but he also tends to just lounge around his quarters without a shirt and such.
Beam Me Up, Scotty!: He never said "It's life, Jim, but not as we know it"; that's from Star Trekkin'. The closest he ever came in canon was the episode "The Devil in the Dark":
Spock: Within range of our sensors, there is no life, other than the accountable human residents of this colony beneath the surface. At least, no life as we know it.
Bizarre Alien Biology: Principally his green blood and the fact that his heart is where a human's liver would be. The latter enables him to survive being shot in the back with a flintlock rifle in "Friday's Child".
Blue-Green Blood: Not explicitly stated, but his father is a prestigious Federation Ambassador, and T'Pau, one of the most powerful people on Vulcan, officiates at (what should have been) his marriage. He also notes that the large estate where the ceremony takes place has been in his family for over two thousand years.
Boomerang Bigot: Is half-human, but most of the time solely embraces his Vulcan heritage and is scornful of human ways. This was later explained in backstory due to his relationship with his father and growing up on Vulcan, and he mellowed in his later years.
Catch Phrase: "Fascinating", accompanied, of course, by...
The Creon: Spock is this, almost to the letter. He only takes command of the Enterprise once Kirk has been Kicked Upstairs, and gives it back almost immediately when the opportunity arises. And, being already a captain and in command of the Enterprise, Spock never gets his own commission: he keeps his position as first-officer under Kirk for several more movies!
Surprisingly, Spock's mirror-universe counterpart is exactly the same on this - and even explicitly states his reasons (in "Mirror Mirror").
Deuteragonist: A natural result of his popularity with fans; originally, the show was intended as having plots about "Kirk and X", where "X" would be a different character each week; many of the early first season episodes follow this formula, but gradually "X" and "Spock" became interchangeable.
Fantastic Racism: A victim of this trope, as well as a mild subscriber (towards humans).
Forgets To Eat: Occasionally. While never shown, in "Amok Time", McCoy uses the fact that Spock hasn't eaten for three days in an attempt to convince Kirk that something is wrong, and Kirk dismisses it as simply being Spock in one of his contemplative phases. Another example is "The Paradise Syndrome", where Spock hardly eats for weeks while studying the obelisk.
(After Kirk informs a man that he will be taken from his planet with or without his cooperation) "Should I get the butterfly net?"
Determinator: Where Scotty wouldn't roll over and die on keeping the ship together, this man refuses to just let his patients die if he has any means to save them.
In-Series Nickname: "Bones" is actually short for "saw-bones", an archaic term for a surgeon. It was originally intended as the nickname of Dr. Boyce from "The Cage", but was never used in that episode, making it available for McCoy.
Knight in Sour Armor: He's grumpy, sarcastic and has little respect for authority (With the exception of Kirk). But when the chips are down, You can always count on him to do the right thing.
More Hero than Thou: In "The Empath" when aliens offer Kirk the choice of sacrificing McCoy or Spock, McCoy takes out Kirk with drugs. Spock is glad; since this leaves him in command, he can make the sacrifice himself. McCoy proceeds to drug him as well and sacrifice himself.
Resignations Not Accepted: At the beginning of the first movie, has retired to private practice, and is called back into service against his protests on Kirk's request.
What Could Have Been: An episode exploring his Backstory was planned and shelved at least twice. One of the main points (that he joined Starfleet as an established MD after a nasty divorce) finally saw the light of day in the 2009 movie.
Lieutenant Commander Montgomery "Scotty" Scott (James Doohan)
Beam Me Up, Scotty!: Scotty is universally remembered as complaining that the engines "cannae take much more ah this, Cap'n", for fear that "she's gonna blow", or some variation thereof. He's also known to protest that "ah doon have th' pow'r, Cap'n!" He never used any of those phrases on the show; they're cobbled together out of a dozen different lines from different episodes, and have become ubiquitous in parodies ever since.
He also said "Ah cannae change the laws of physics", and not "Ye cannae". That's from Star Trekkin'.
Berserk Button: If you insult the Enterprise, you better take his hint (said through gritted teeth) of "Don't you want to rephrase that..."
Companion Cube: If Kirk saw the Enterprise as a demanding wife, Scotty saw the ship — particularly her engines — as no less than a child ("My bairns! My poor bairns!").
Dangerously Genre Savvy: Whenever he was left in command of the Enterprise. There's "Fool me once, shame on you, fool me twice, shame on me," and of course the time that he receives a word message from "Kirk" and the first thing he does is run it through a voice analyzer which proves it wasn't really Kirk. Do not fuck with Scotty.
Gadgeteer Genius: Can MacGyver just about anything on his own, but particularly shines teamed with Spock. The two of them could turn the most obscure theory into a way to save the day.
Canon Immigrant: Her first name "Nyota" was used in the non-canon novels for decades before finally being made official. Very early Trek guides suggest that "Penda" was considered a possibility by the fans.
Fake Nationality: Uhura is from the "United States of Africa", but Nichelle Nichols is American (as is Zoe Saldana in the reboot).
Meaningful Name: "Uhura" is derived from "Uhuru," which means "freedom" (which carried a strong Reality Subtext in the 1960s), while "Nyota" means "star".
Beam Me Up, Scotty!: Don't expect to ever hear Sulu say "Oh, my." That's George Takei's personal Catch Phrase. Sulu himself was the only regular who lacked a memorable Catch Phrase or Verbal Tic, one of the reasons he didn't show up in too many parodies (and when he did, he was usually the Straight Man). More recently, given Takei's predilection for Adam Westing, parodies of Sulu are basically parodies of Takei (including the Camp Gay antics - see below).
Canon Immigrant: His now-canon first name "Hikaru" was given to him in the non-canon novels by Vonda Mc Intyre. Very early Star Trek guides suggest that "Walter" was considered as a possible first name during the show itself, but never officially used.
Fake Nationality: Averted, for the only time in all series. Sulu is Japanese-American from San Francisco, and so is George Takei. Played straight in the 2009 film.*
They were leery of casting an actor of non-Japanese descent until Takei himself assured them that it would be all right, claiming that the character represents all of Asia (note that Sulu is not a Japanese name). This paved the way for Korean-American John Cho to assume the role.
In some of the non-canon novels, Sulu explains that his background is mixed, but primarily Filipino and Japanese.
Katanas Are Just Better: Averted in "The Naked Time". Sulu was originally supposed to go on his rampage with a samurai sword, but at Takei's request to do something less stereotypical, it was switched to an epee.
Sadly played straight in the reboot movie - it's not exactly a normal katana, but it seems clearly intended to invoke this trope.
Why Do You Keep Changing Jobs?: Initially the show's creators couldn't make up their mind what to do with Sulu and he featured prominently as a botanist of all things before becoming the helmsman.
Word of Gay: Inverted. After Takei came out of the closet, many people assumed Sulu was also gay. Takei has denied that in interviews, claiming Sulu was/is straight.
As an interesting coincidence, Sulu is the only one of the six male regulars who never had an on-screen love interest, so there's no "proof" either way (Mirror Sulu, on the other hand, is obviously attracted to women, as Uhura can attest).
Chekov's Gun: Often seen with Chekov, especially on landing-party duty. Like Chekhov's Gun, if it makes an appearance, it will most likely be used by the end of the episode or movie.
Sixth Ranger: Subverted. Chekov didn't appear on the show until Season 2, but apparently served on the Enterprise long before he appeared, because in the second movie, Khan recognizes Chekov, apparently having met him in the Season 1 episode "Space Seed".
Walter Koenig's explanation for how they met is that Chekov actually was serving aboard the Enterprise but was on duty during the night shift, and he and Khan met off-screen. The circumstances of their meeting were thus: Chekov was using the bathroom and he was taking an inordinately long time, and Khan approaches that very same bathroom, needing to use it. Finding it occupied, he soon loses his patience and pounds on the door. When Chekov finally emerges, Khan grabs him and fixes him with a Death Glare, and says "I will never forget your face!"
This is further compounded by the fact that he expended all the toilet paper.
Mad Love: Most of her personality (well, all of it, really) centers around her unreciprocated crush on Spock. Think of her as an in-universe Spock Fangirl. Unlike many of her real-life counterparts, she doesn't seem to be a Yaoi Fangirl.
No Rank Given: In the series, Chapel was always addressed by her position rather than her rank. She is formally promoted to Lieutenant later on in the five-year mission, and by the time of the first movie, has an MD under her belt, and is prepared to assume the role of Chief Medical Officer. We can therefore assume that, especially given her position as Head Nurse, she was a junior officer (probably a mustanged Ensign, given her backstory).
Real Life Writes the Plot: Majel Barrett was the girlfriend and eventual wife of Gene Roddenberry, which may explain why we saw Nurse Chapel so much.
Hypercompetent Sidekick: Implied—there are several references to her ability to keep Kirk from being swamped in paperwork, and one to improvising with a phaser when the food systems won't provide hot coffee.
Ms. Fanservice: The original media package described her as having "a strip queen's figure that a uniform can't hide." Not that those uniforms hide much, but whatever.
Satellite Character: Has no significant interaction with any character other than Kirk.
Mauve Shirt: Because he was the only recurring redshirt not played by an extra, he usually had much more dialogue than other redshirts, a consistent name and position on the ship, and was allowed to play an active role in the plot (see "The Doomsday Machine" or "Mirror, Mirror" for examples).
Teleporters and Transporters: Contrary to popular belief, he was the Transporter Chief, not Scotty. Like other redshirts, he was occasionally seen on the bridge, though usually he was explicitly pinch-hitting for someone else (as in "Who Mourns For Adonais?" when Spock has taken command and Chekov is in the landing party, and Kyle mans the science station).
Kevin Thomas Riley (Bruce Hyde)
Ascended Extra: Actor Bruce Hyde was cast as a crewman with a significant part in "The Conscience of the King" without anyone realizing he had also played uber-Irishman Riley in "The Naked Time". When the producers finally realized this, the script was hastily re-written so that Hyde played the same character in both episodes.
Oireland: Got his "Irish" up when under the influence of the mind virus in "The Naked Time."
Real Life Writes the Plot: The reason Riley never returned after "The Conscience of the King", despite being very popular with fans, was that the actor left to become a hippie. Yes, really. Remember, this was 1967.