To prevent an all out war between three nations, the Demon World had to set up a Ass Kicking Equals Authority Tournament where the winner would be crowned king of the Demon World.
Rosario + Vampire has this as a running theme in the Youkai World, where there is a pecking order based on how strong you are, and it's a ruthless Social Darwinist.
High School Of The Dead has a universe that kills off the weak or zombifies them, leaving the world populated by badasses. In fact, being one has pretty much become a bare minimum requirement for survival.
The world of Dragon Ball where everyone is a super powered martial artist, and even the comic relief Muggle Mr. Satan/Hercule is a Badass Normal who can kick any non-powered human's ass.
Baccano. All named characters can fight. All exceptions learn.
Durarara!!. Half of the cast is outright Crazy Awesome, while the other half is badass in one way or another. No exceptions. And since 'Durarara!! takes place in the same universe as Baccano, this makes sense.
In Magical Girl Lyrical Nanoha, the world of Midchilda is a non Crapsack World example. Generally, the rule is that if it comes from Midchilda and has a name, it will be able to annihilate you. It doesn't matter whether you are talking about five year old girls, ferrets or six inch cute mascots. Or books.
Pokémon Special, a world where humans are more likely to be fighting along side of their Pokémon instead of just hanging back.
Soul Eater. Pretty much every single character who isn't cannon fodder for the kids' Gotta Catch Them All schooling is badass at some point in time.
Noblesse Anyone (attractive) in the series will inevitably be Badass but especially the Noblesse, who can easily cut through buildings when they fight.
Dorohedoro. You can't be non-badass and survive in a world where Devils go for a walk when they're bored, much less in a city where the yearly Zombie Apocalypse is a fundraising event. It's good that Death Is Cheap, otherwise Anyone Can Die would have slaughtered most of the main cast by volume 8.
Mahou Sensei Negima!, or at least the residents of the Magical World. The most Badass of them all? Evangeline. And that's saying something.
In Fairy Tail, 10% of the world's population is made up of mages, and there are surprisingly few Squishy Wizards.
Noir depicts a village in France where everybody, with no exception (children, old women and nuns included), is an assassin trained to mass-murdering or die in attempt. As just are the main characters, Mireille and Kirika and most part of the other characters as well.
Bleach. Any named character who resides in Soul Society or Hueco Mundo is able to kick your ass. Yes, even the wimpy White Mage, and yes, even the guy who transforms into a pink pumpkin. To say nothing of the human characters.
Sin City. Even the Comedy Relief bad guys, Shlubb and Klump, can withstand an explosion from close-range.
But come on, the Yellow Guy is anything but badass.
Scott Pilgrim. At first it seems like only a few people can really fight, but it becomes pretty clear that almost every minor character or random background extra could probably throw down with some bizarre fighting style or weapon if sufficiently provoked.
Jim Valentino's normalman features the planet Levram, where everyone has super powers. Everyone, that is, except the eponymous character normalman. And as the series progresses he gets increasingly badass without ever gaining super powers.
And even side-characters and civilian allies can step up to the plate without being bitten by a radioactive anything. J. Jonah Jameson may be a jerk but he won't back down from Doc Ock when his people are in danger. Mary Jane does not make a cooperative damsel in distress (outside the movieverse.) The X-Men's scientist friend Moira Mc Taggert once pulled out a machine gun to battle a monstrosity calling itself Kierrok the Damned. Lois Lane knows kung fu. The list goes on.
The Malazan Book of the Fallen series has badass characters in droves, ranging from Physical Gods to Badass Normals. Among the hundreds of named characters it would be easier to list who isn't a badass. Those would include... well... the Mhybe and Challice D'Arle. That's about it.
Belisarius Series: Almost every character is a badass. Aside from the title character, his wife is a retired hooker who is somehow able to kill half a dozen assassins with a meat cleaver and a cauldron of stew, his wife's best friend is a spymaster of spymasters, the seeming Distressed Damsel can kill men with her bare hands, and convince her former captors to pledge loyalty to her; her husband is one of the two greatest warriors in India. And on and on.
Discworld. If you intend to mess with someone here, make sure they're not witches, wizards, dwarves, trolls, Mrs. Cake, demons, gods, gnomes, Mrs. Cake, werewolves, vampires, pictsies, heroes, Mrs. Cake, assassins, monks, Sir Samuel Vimes, Death, Susan Sto Helit, the Luggage or last, but not least, the Librarian (and Mrs. Cake). It's a wonder that anyone else is left in the place.
An entire town called Bad Ass appears in Wyrd Sisters. Unsurprisingly it is the home town and base of Granny Weatherwax. Visitors to Lancre have been warned. Apparently a donkey once stopped midstream and refused to go either forwards or backwards. But that's their story.
Possibly a Shout Out to Shea and Wilson's Illuminatus! trilogy, in which the Texan town of Bad Ass is a throwback to earlier ornery Confederate ways and has a robust attitude to all those northern carpetbagging liberal sissy notions such as desegregation. Bad Ass is an embarrassment to the rest of the USA, which uncomfortably realises that Badass is how the rest of the world sees the whole of America.
World of Badass is a literal description of what happens to the setting of Men. There are only eleven people left on the planet, all men, and they are all incredibly damned awesome.
In order to be a Time Scout, you have to be a badass. Hell, just to associate with a time scout will probably require you to be a badass. The only people who aren't badasses are tourists. They're just kind of annoying.
Warrior Cats. Yes, nearly every single one of the 700-some characters is trained to fight and can hold their own in a battle.
World of Badass is an excellent description of Barsoom where the Mad Scientists carry sword; the Damsels In Distress are likely to slip a dagger between your ribs and little old men can give the best swordsman on two planets a fight to remember.
Live Action TV
Alias. Even relatively dorky characters like Mitchell got to save the day or make sassy remarks while being horrifically tortured from time to time.
Hercules: The Legendary Journeys. Almost every character in this show, be they princess, middle-aged mother, or barmaid, seems to be a rather good fighter. (Salmoneus may be an exception.) This rule seems to also apply (perhaps to a lesser degree) to the spinoff Xena: Warrior Princess.
24. Put it this way: Kim Bauer has fought off psychotic kidnappers, smashed her abusive employer in the face with a crowbar, broken out of police custody by setting fire to the transport van while she's in it, fought off seasoned, bloodthirsty war criminals with a hot coffee pot, and more. In any other series? She'd be a bona fide Action Girl. In this one? She's a Damsel Scrappy. That's right - these are the accomplishments of the LEAST badass person in the main cast. And then there's Behrooz Araz, a doe-eyed teenager, who enacts some seriously badass Shovel Fu on Day 4.
Babylon 5: This is a show that has diplomats that can endure torture, break chains, personally command battle fleets, or even out- Chessmaster multi-million year old space demons. It also has an outpost commander who goes back in time and becomes a Messianic Archetype. Not to mention Battle Butler s that can pick up a man with one hand or fiendishly arrange for the prisoners to be lost in paperwork and found somewhere where they won't be exterminated.
Professional Wrestling itself is a world of badass. Many wrestlers are legitimately badass outside of the ring, and some people have found this out the hard way.
BIONICLE. There are vicious, the Makuta, the brain washing bohrak, a sleeping god, corrupt politicians, and freaky looking vehicles. To deal with it, they have Toa warriors. Hell. Yes.
Darwin's Soldiers - With few exceptions, everyone, everywhere can kick serious ass.
The Warhammer 40,000 universe, of course. This happens largely through a twisted form of natural selection; the insufficiently Badass simply die in droves at the hands of the rest.
Warhammer Fantasy, although in this case it's one-third natural selection, one-third the will of the gods, and one-third taking on Bloodletters without semiautomatic rocket grenade launchers or tanks the size of small cities.
Exalted. If your character can't be described as an utter Badass, you are doing it wrong. You know that you are living in a World of Badass when the fairies are soul-eating Eldritch Abominations, and are some of the weakest beings in the setting.
Feng Shui, naturally, since it's based on action movies, especially Hong Kong ones.
Video Games
In any given Fighting Game all the characters can kick your ass.
The Fallout series, bare minimum, requires EVERYONE be an Action Survivor, and if you want to enjoy a healthy lifespan in a post apocalyptic world where quite often Everything Is Trying to Kill You, being some sort of badass is about the only way to enjoy most of your natural lifespan.
Metal Gear, where everyone is a hard-boiled double agent who may or may not have supernatural abilities. A world where a women gives birth via a messy c section and then immediately leads the charge at Normandy on D-day.
Devil Survivor 2 recently took this Up to Eleven. In other SMT games, if you didn't have demons, demon power, or could otherwise fight them in some way, you were screwed. In this game, though, not only is demon summoning ability available to pretty much everyone worldwide as long as you have a cellphone (which IRL and ingame easy to get and very widespread) and a free downloadable app, even that isn't necessary in one level where unarmed, non demon summoning civilians are fighting demons and demon summoners and doing pretty well.
Not to mention the fact that the first game had an ingame justification/Hand Wave on why normal unarmed humans could hope to stand up to demons in a fight and not be killed in a single hit from them: no such thing exists in the second game, implying that everyone's just that strong normally.
City of Heroes for the most part has a rather large percentage of the population being superheroes and/or supervillains.
Devil May Cry: there isn't one character that isn't an absolute Badass. (Unless you count the animated series.) (Actually there is one character in the games that isn't badass: Kirye.) Even normal humans like Lady have ridiculous stamina, when they're not outright Made of Iron.
Fire Emblem, where a little girl can with a little experience and luck destroy an entire army by herself.
It's H-Game parody, Sengoku Rance, basically is the same formula, just with a different gameplay engine and tons of estrogen due to massive amounts of Gender Flip (though non of women are less badass as a result}.
Australia in Team Fortress 2 is a Country of Badass: the men fight everything they can get their hands on, the women have epic moustaches, and the girl scouts have been known to wrestle bears.
Mabinogi: Even aside from the PCs, you see a lot of memory sequences (and actual fight scenes) of NPC army characters being extremely badass.
The Mass Effect series is a definite aversion. You very frequently run into completely ordinary people - scientists, merchants, random civilians - who are out of their depth in even a fistfight (Though the Krogan homeworld plays this straight in a very literal way). Usually, it puts the typically badass gameplay in sharp relief.
Dragon Age II, more so than the first game. Fewer cowering screaming people, bigger dragons, and nobody flinches from battling the guy that according to the tales killed a High Dragon with a rusty spoon.
Touhou is set in Gensoukyou, a realm that has become the nexus of the planet's magic and badass. When a character that can freeze their opponent solid in an instant and another that can shatter boulders with their fists are mocked by fans and other characters for being too weak, then this trope is inevitable.
Guild Wars is a game where major characters who can't fight are extremely rare.
Resident Evil oh very much so! Ashley from Resident Evil 4 even has one or two moments and she is a Damsel Scrappy.
Arc The Lad is a world where even a pathetic coward in the Seyran army's drum corps can become a fearsome One-Man ArmyMagic Knight. The real heavy hitters on every side are outright Persons of Mass Destruction. And it takes thousands of years and entire civilizations composed of these people to defeat the Big Bad.
In World of Warcraft, even the lowliest, non military NPC you come across will generally have as many hit points as the big, tough monsters you fight, and be able to dish out nearly as much damage as said monsters just with his bare fists.
Pretty much any named character who's done something relevant is likely to be a badass - such as Illidan, Malfurion, Tyrande, Jaina, Thrall, Arthas, Uther, Varian, Fandral, Archimonde, Kil'jaeden, Medivh, Maeiv...
Asura's Wrath is MADE of this trope. From a rampaging demigod whose strenght seemingly has no limit and who gets stronger the angrier he gets, a deity that becomes bigger than the Earth itself, to another one who has a sword that can extend all the way from Earth to the fucking moon, and pierce right THROUGH IT! And that's just the three characters revealed in the demo.
Urban Rivals. When 22 factions are vying for control of the city, even the weakest combatants have to be Badass Normal.
Visual Novels
The Nasuverse itself. If they have a name, they have badass points:
In Fate/stay night every main character has severe badass credentials by the end except Shinji, really. Yes, even Ilya and Sakura. Fate/hollow ataraxia barely changes the cast, but even those few it adds are amazing, such as Bazett Fraga McRemitz, a human who can go toe to toe with Servants — in fact, she has her own Noble Phantasm, which only Servants are supposed to have.
Angel Notes, a virtually unknown piece of work within the Nasuverse, involves swords so long they can carve out chasms in the earth, and humans slaughtering an Eldritch Abomination. World of raging badass indeed - then again, it did give us Archer.
In Maji De Watashi Ni Koi Shinasai, there are very few characters who can't fight, and many who takes it to a ridiculous degree. The anime even opens with a war game which includes the entire school. The same event is also in one of the routes.
Webcomics
Girl Genius comes very close. Every character from top to bottom seems to get at least one moment of absolute Badass, from the protagonist, to her Love Interest, to a traveling show full of minor Sparks, to some random soldier who woke up to find his airship on fire, to that pretty pink princess.
In the world of Axe Cop, if you have a name, chances are good that you are either a good guy with superpowers or a bad guy about to be destroyed.
The Adventures of Dr. McNinja is pretty much this combined with Rule Of Cool. Ninja doctor with a velociraptor-riding, revolver-toting bandito sidekick. Whole family of ninjas. Pirates that fly around in their airships. A zombie-killing chrononaut/astronaut for a mayor. The list of badasses goes on.
One story involves an army of primitively-armed humans attacking, successfully at first, a fortress full of gun-toting dinosaurs. Some of the humans turned into giant lumberjacks and wrestled the dinosaurs to death. In case it's not obvious, insane badassery is pretty much the entire point of this comic.
Homestuck: If you've managed to get into the Medium and you're not badass already, you will be soon enough.
In a more literal Crapsack World example, Alternia. Even surviving past infant-hood in Troll society requires a certain degree of Badassness, since wigglers are put through a series of harrowing trials immediately after they hatch. It says a lot that a thirteen year old blind girl from Alternia is one of the most badass characters in Homestuck, and that even the wimpiest among the trolls has strong psychic abilities that allow him to tame and raise a virtual army of monsters.
St. Louis is a city of badass in Lackadaisy. All the characters have their moments
Here's a list: Rocky Rickaby, who dances in and out of danger and gets in all sorts of trouble; Aunt Nina, a badass grandma; Freckle McMurray, who goes from quiet ex-cop to "murders three recurring villains with a tommy gun while laughing like a maniac" almost immediately after finding the Lackadaisy; Mitzi May, who is simply an Action Girl; Dorian "Zib" Zibowski, who is a total badass without ever picking up a weapon; Mordecai Heller is, well, Mordecai Heller and the list goes on.
Schlock Mercenary has a truly fascinating example. The galaxy is just filled with Mooks for Tagon's Toughs to savage, and Worthy Opponents to return the favor. But the Toughs themselves have a contagious case of Badass. They pick up a (ir)reverend (because he was the sole applicant) and a doctor (based on her cup size). The reverend is soon skewering enemy eyeballs with a fencing foil. The doctor ends up leading troops into curbstomps and delivering speeches "Like Patton with boobs". They grab a bunch of loser thugs off from a Wretched Hive on a Scavenger World. The one with no arms can float like a butterfly(with gravitic assists) and sting like a bee(as in wrestle entire gangs with her tongue). They grab a Wrench Wench off a UNS battleplate that wants to get rid of her. She slaughters mobs singlehandledly (with Powered Armor and Post-Dramatic Stress Disorder). Join The Toughs. Be Badass.
Lyle Phipps manages to invoke this trope in Great. Everyone he interacts with is inspired to become awesome in what they do because of him.
Shock, on Stickpage.com, is a stick animation based in a world so badass, that ''this'' is what happens when you want to apply for a position AS THE FUCKING JANITOR
In Avatar: The Last Airbender, you can count the characters who aren't badass on one hand. Even most of the ones who don't bend make up for it. To wit, one episode opens up with a random old guyin a fight with a platypus-bear.
Well, not really a fight. He just smilingly sidestepped the platypus-bear's every attempted blow.
Sequel series The Legend of Korra involves a brewing city war between the benders and the badass normals and a main character who is already possibly the biggest pre-debut Memetic Badass in the history of 21st century Western cartoons yet can still be driven to tears.
Cybertron, homeworld of the Transformers. Even the planet itself is badass, what with being a badass god, Primus in disguise. Even the least badass of Transformers is usually still a twelve foot tall car/robot hybrid with built in missiles and stuff.
The least badass Transformers are probably either the Mini-cons (until they unleash their full Unicron-given powers and become a giant glowing green Unicron and battle the Chaos-bringer hand-to-hand or G1 Wheelie (except in the versions where he lived on a Death World all his life and has a necklace made of Sharkticon teeth. And still does the annoying rhyming thing which was made cool).
In Fairly OddParents, Timmy wished that his life would be like an action movie. And like an action movie, things went from bad to worse.
The Boondocks. Though Huey's portrayed as a martial arts expert, he's constantly matched or bested by senior citizens, psychotic women, and even Uncle Ruckus.
Ruckus: "What? You think you the only one to learn the ancient and deadly art of the Nunchaku?"
The entire cast of Gargoyles. The leastBadass character would probably be the mutated flying Cat Girl who can shoot electricity out of her hands. Yeah.
