As a class-based shooter, every character in Team Fortress 2 has a fixed set of equipment and abilities, and a role to play in propelling the team to victory. Each class is distinct in looks, personality, and accent, and has a set of weapons and equipment unique to them.
Battle Cry: Each class has a few, and everyone yells at the beginning of a round.
Because I'm Good At It: Most mercenaries who feature in the interview-style "Meet the" videos offer this justification for why they do what they do. Even the "Meet The Spy" video, the first to break the interview format, can be considered an inverted version of this trope.
Beware the Nice Ones: Some of the crew can be considered very amiable, polite, and even charming, but all of them are mentally unbalanced, bloodthirsty lunatics. Taken to the logical extreme with the Pyro.
Bunny-Ears Lawyer: They're all mentally ill, and of dubious morality, but all of them are very good at what they do.
Cast of Snowflakes: It's uncommon to see a First-Person Shooter with five classes distinguished by anything more than different weapon loadout, let alone nine, viable, completely distinct classes. The amount of work this took to balance could (literally) be summed up as "1 year for each class." According to the game's commentary, the characters were deliberately designed so that they could be distinguished from one another simply by their silhouettes.
Comedic Sociopathy: All nine classes segue into comedic sociopathy quite often, but most commonly when they dominate an opponent.
Medic: Can you feel the schadenfreude? Scout: He-hey, look, you shapeshifted into a dead guy! Pyro: AH HA HA HA HAHAHAHAHAHA! Heavy: I am amused by entire eetty-beetty-teeny team!
Also, the Schadenfreude taunt, introduced in the ‹ber Update, allows anyone to take joy in the misery of their enemies.
Difficult but Awesome: Each class has this to varying degrees and in different ways. This means that players tend to get attached to a single class that they've become good at, and new players expecting their FPS skills from other games to transfer to TF2 end up disliking or even hating the game because they're not immediately good at it.
Evil Laugh: Every class has a few for dominating, revenge, and getting multiple kills. They also all have a Schadenfreude taunt (mentioned above).
Face Death with Dignity: During "Expiration Date" they all take the news that they have three days to live incredibly well, almost to the the point of ambivalence.
Family Values Villain: When they're not on the job, many of the mercs try to be this, handing out human molars and inordinate amounts of blood money to trick or treaters, defending Smissmas shoppers from inhuman monsters, escorting unarmed noncombatants through deadly robot hordes, and helping children to conquer their fears through teaching them to commit murder. Moral Dissonance is invoked, lampshaded, and played for laughs, especially in the case of the Pyro.
Demoman is an interesting case. He lives with his blind mother so he can help take care of her. His mum however knows full well what his job is and actively encourages it (after all, it's been in the family for generations).
Informed Flaw: Interestingly, while their sanity (or lack of) isn't questioned, they have been described as "mostly having below-average IQ's" by Miss Pauling, and as "idiots" by Helen the Administrator, though each of them later displayed smarts ranging from Genius Ditz to Ditzy Genius level. A later comic shows why she holds them all in such disdain: She believes them to be just like the lead poisoned idiots of Teufort, while Miss Pauling has secretly been providing all of them with bottled water, save Soldier, who didn't bother listening to her warnings.
Large Ham/World of Ham: Just about everyone in the game, but especially Gary Schwartz, the voice of the Heavy and the Demoman.
"HAHAHAHAHAHA!!! CRY SOME MOOOOOOOORE!!!"
"THERE CAN BE, ONLY OOOOOOOOOOOOONE!"note eye...
The Leader: Actually, it's not really clear. Heavy has the best case as he's the face of the team in most media and is generally depicted as the one the others rally around. Soldier and Scout are bossy enough to possibly think of themselves as this, although Soldier probably has more claim to the title than Scout does and the others are more likely to humor him than Scout. During actual gameplay, the Medic player usually takes this role in more competitive formats, while in public servers it could really be anybody, depending on a few different factors (scoreboard position, competence, willingness to take charge, etc.) That's if the team doesn't just go the democracy route and do whatever most people agree on, and that's only if people bother listening to each other at all.
Legacy Character: Judging by the Engineer Update and its comics there have been at least three of each mercenary - a hidden picture in the Engineer update shows a retconned version of the Team Fortress Classic in World War I-II versions of their uniforms, and another shows the TFC BLU Engineer letting his son (Dell Conagher, the current BLU Engineer) try on his goggles. As of A Cold Day in Hell, the classic team have canonically appeared in the TF2 universe as a band of older mercs brought out of retirement, cemented by the catch-up comic explicitly naming them as the predecessors of the modern team.
Professional Killer: Whether the team is professional in the "gentlemen" sense of the word is... well... debatable, (See directly below), but the team does what they're paid to, and they do it very well. Best summed up by the Engineer's quote to a rival Medic:
"I'm a killer of men, Doc. That's the God's-honest truth."
Required Secondary Powers: According to "Meet the Medic", every class had to have special heart implants in order to use the ‹berCharge. In the case of the Heavy, his heart had to be replaced with a much larger one after his first heart exploded from the power of the ‹berCharge implant.
Sociopathic Soldier: Not just the Soldier. They all enjoy killing their enemies and making fun of them, and revel in their jobs.
Spell My Name with a "The": They're referred to this way by the blog and other website materials, but all dialogue (in-game and in the comics) lacks the articles.
Surrounded by Idiots: With the possible exception of the Soldier, the entire team is put in this position due to the people of the nearby town of Teufort having been rendered a pack of sociopathic idiots from generations of drinking tainted river water.
Unscrupulous Heroes: Each team member has a few people whom they care for dearly (each other included) and a few spare standards, but otherwise won't think twice about doing dirty deeds for high prices. The single redeeming trait these otherwise sociopathic maniacs have in common is that they wholeheartedly care for their families, friends, and loved ones.
Even Non-player character SAXTON HALE has revealed that despite his obvious testosterone poisoning, he just doesn't have it in him to strike a little girl.
Villain Protagonist: The comics show the civilians of Teufort see them as destructive maniacs and it's hard to argue with them. To the point that they put Scout and Spy on death row for doing their jobs in "Ring of Fired."