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 eety-beety-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).
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.
Informed Flaw: Interestingly, while their sanity (or lack of) isn't questioned, they have been described as "mostly having below-average IQs". However, while Soldier and Scout are definitely idiots, everyone else has been shown to have quite a bit of intelligence to some degree. Demoman clearly is knowledgeable concerning elements and chemicals required to create explosives (a good demoman would probably have quite a bit of knowledge in chemistry), Pyro managed to turn an engineering business into a million-dollar success story in "Ring of Fired", Heavy has a PHD in Russian literature (that's Dr. Heavy to you), and Engineer, Medic, Sniper and Spy basically speak for themselves. Of course, how much common sense each of them have individually is another matter entirely...
Heck, even Soldier and Scout show signs of intelligence here and there. Scout knows who Hippocrates and H.P. Lovecraft are, and Soldier's educated enough to (somehow) have become a lawyer, a priest, and an exorcist.
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...
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.
Professional Killer: Whether the team is professional in the "gentlemen" sense of the word is... well... debatable, (See directly below), but the team do 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.
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 little 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.