"They're a wonderful, friendly people--as long as their bellies are full and their holosuites are working. But take away their creature comforts...deprive them of food, sleep, sonic showers...put their lives in jeopardy over an extended period of time...and those same friendly, intelligent, wonderful people will become as nasty and violent as the most bloodthirsty Klingon."
Humans Are Special: Tuvok deconstructs this in the Voyager episode "Flashback". When serving on the Excelsior under Captain Sulu, he was initially cordial but left after their first mission because he felt humans were trying to force the rest of the galaxy to be like them. Even in the episode itself, Sulu and Rand seem to view Tuvok as a Replacement Goldfish for Spock.
Planet of Hats: Averted; we're the only planet that doesn't have a hat.
Several characters have commented on how relatively fast humanity expanded compared to other species and how quickly humans tend to pick up a skill or job. Humanity's hat seems to be taking everything Up to Eleven.
Then again, we're clearly heading this way. Whenever the cast finds themselves stranded in Earth's 20th/21st centuries, they're always dumb struck by the amount of cultural diversity. Janeway even faints they're so much.
We All Live in America: Or at least Western European; all other cultures seem to have died out. All the names are surname-last, alien cultures that borrow elements from other Earth cultures are seen as mind-blowing, and the French all sound like grumpy Englishmen.
"Live long and prosper."
The Atoner: They were once a Proud Warrior Race that was probably even fiercer then Klingons or humans. Horror at the results of this made them turn to the teachings of Surak and follow the rather painful creed of the time of the show to control their violent emotions.
And Romulans are Vulcans who did not follow Surak. Nuff said.
Actually, they are usually portrayed as Worthy Opponents and Noble Demons in both, especially in the latter when in at least one episode Archer gets a Klingon lawyer who serves as a Deconstruction of this (helpfully played by Deep Space Nine's General Martok, Worf's buddy), saying that neither of his parents were warriors and lamenting the way his people are becoming less civilised, as well as less honourable than they claim, but denying that every Klingon is a savage barbarian.
Always Someone Better: At the end of the day, they're usually presented as the most powerful fighting force in the Alpha Quadrant. Not the smartest but definitely the strongest.
Depending on the Writer: Are they space vikings? Space samurai? Petty thugs? Religious zealots? Note that whichever one they are can change mid-episode. The only consistent aspect of their culture is that they respect shows of great strength.
All but mocked in Star Trek vs. Transformers where it seems that Megatron and Starscream have no idea how the Klingons think and simply think showing off how strong a Cybertronian is all that they need to win the Klingons' allegiance.
The Drunken Sailor: And even the greatest of Klingon heroes are not allowed to receive their honors until they have proven that they can hold extreme amounts of Blood Wine.
Rated "M" for Manly: Their idea of a bachelor party is four days of Macho Masochism. Their idea of a honeymoon is going on a hike through the nastiest terrain in the galaxy. Their idea of a joyous wedding night is for the happy couple to gleefully beat each other to a pulp. And their idea of a wedding ceremony is to tell how two mythical Klingons showed their love for each other by teaming up to sack and destroy the heavens. Isn't that romantic?
Too Dumb to Live: No matter how many times they learn you can't trust Romulans, one of them will.
"We are creatures of duty, Captain. I have lived my life by it. Just one more duty."
Always Second Best: Particularly in TOS and TNG. They'll try to outwit the Federation and the Klingons but never quite make it.
Arch Enemy: On TNG. Not as powerful as the Borg, not as ruthless as the Cardassians, but more recurring than either and are behind half the evil schemes in that series. Arguably this again in Enterprise.
How the Mighty Have Fallen: Following their sun going supernova, the once mighty Romulan race seen in Star Trek: Picard is reduced to various holdouts of civilization, some of whom don't have the resources to continue warring. Even some of their senators became simple peasants.
Jerkass Has a Point: Their entire civilization disproves Sarek's belief that only total logic could save the Vulcan race.
Man Behind the Man: If some villain is implied to have a secret benefactor, the benefactor will probably be the Romulans. Especially if the villain is a Vulcan or a Klingon, just to show how traitorous or gullble they are as both species regard the Romulans as long-standing enemies.
Strawman Emotional: Disagreed with Surak's logic and left to start their own, more amoral, militaristic society.
Though overall, they are still very composed and disciplined. Ironically despite their imperialistic empire, they seem to contradict the idea that Vulcans who don't control their emotions are a dangerous menace, since on a personal level they rarely if ever violently lose their temper or hint at uncontrollable emotions. In-universe this is attributed to their lack of suppression; there is no emotional build-up to blow off when they lose their cool.
Wild Card: Just as likely to stab you in the back as they are to help you. It's why Starfleet didn't ask them for help against the Borg and was hesitant to do so against the Dominion. There's a 50/50 chance the Romulans would have helped or just propped up their feet and watched their enemies kill each other.
Worthy Opponent: Several of the most memorable Romulan characters in the original series, as well as a number of times in the novelizations.
"They were cunning warriors...always had a plan within a plan leading to a trap...it was an honor to kill them."
Remember the New Guy?: The episode they're introduced in, "The Wounded", is said to take place a year after a Great Offscreen War between them and the Federation. Most of the Enterprise-D crew fought in this war yet "The Wounded" is the first mention of them.
Early Installment Weirdness: Originally the Borg were conceived as an organic race that introduced technology into itself at birth. Them turning Picard into Locutus was treated as a unique occurrence. Somewhere around TNG's fifth season, they became the assimilators of organic life they're famous for.
Alternate Universe Reed Richards Is Awesome: In one alternate timeline, they not only kicked the Cardassians off their planet themselves, they took over the Cardassian Union and became a major foe to the Federation.
He Who Fights Monsters: Their mirror counterparts were a Terran slave race. Now they have the Terrans in chains.
How the Mighty Have Fallen: The Bajorans had a golden age some 500,000 years before the 24th century. Come said century and they're only getting by through the kindness of others, most of whom developed long after them.
Early Installment Weirdness: They were originally shaping up to be the new Big Bad of TNG in its early episodes. Once the audience reacted to their design and personalities, they became a mercantile race.
Mad Libs Catchphrase: The Rules of Acquisition, of which there are over a hundred. Possibly the only code of honor the Ferengi follow.
Subverted by the Rules themselves turning out to be another scam -- at least in Quark's dream.
"Would you buy a book called Suggestions of Acquisition?!"
Meaningful Name: The name "Ferengi" is a corruption of the word "farhang," which was a derisive word used in some parts of Southeast Asia to describe European colonialists merchants.
Variations are used across Asia, ultimately all distortions of the word Frank, i.e. somebody from France, mistakenly interpreted to mean all Europeans.
Space Pirate: Their original characterization when they were planed to be serious villains. Implicitly Retconned to be just a few who couldn't make it in "legitimate" business.
Turned on it's head a little though, if Quark can be trusted, in that while Ferengi are greedy as a virtue and sexist/xenophobic as a culture, they've also never taken it to the same extreme that humans have, citing that the Ferengi never had concentration camps, slavery or massive-scale warfare. In particular, Quark states that the Ferengi would have negotiated a mutually beneficial deal with the Dominion, as opposed to the Federation's "Independence at any cost" stance.
Villainous Valour: They take pride in their discipline and prowess and are generally treated tragically rather then as faceless mooks. If they were more chivalrous they would be considered Worthy Opponent s. As it is, even Klingons fear them.