Charge, of All Superheroes Must Die, as well as apparently all of the superheroes who came before the protagonists.
Not surprisingly, many of the veteran crimefighters in Astro City are regular folks coupled with a few gimmicks (Jack-In-the-Box, Crackerjack, Altar Boy, the Black Badge, El Hombre, the Flying Fox), but who have trained themselves up to bullet-dodging levels.
Deconstructed with Quarrel; she constantly realizes that she's a Badass Normal in a world of super-powered beings, armored villains, aliens, and gods, and compensates for it with lots of training — to the point where she cannot sustain any sort of normal relationship because of the commitments required. She's only with Crackerjack because she doesn't care that he Really Gets Around, and he doesn't care if she forgets his birthday.
Played with in the case of Sticks. In his home of Gorilla Mountain, he's just a typical — and disinterested — soldier in gorilla society. In Astro City, however, his strength, training, and prehensile feet makes him a dangerous opponent to anyone who tries to exploit him.
in "The Dark Ages", Charles and Royal Williams eventually grow into this role through a combination of physical training and gear appropriated from Pyramid.
Black Hammer has Abraham Slam. In a world full of superpowered heroes and villains, Abraham Slam is a normal man who fights crime with world-class boxing skills and the occasional gadget.
Black Moon Chronicles: Murata, unlike most of his allies, does not have any inherent magical powers (Wismerhill, Hellaynnea) or incredibly size and strength (Ghorghor). He's just a very well-trained human Samurai.
Golden Age Daredevil was just some guy who threw around a boomerang and fought crime. And yet, he was capable of regularly fighting a size-changing sorcerer and pulling off acrobat feats that should not be possible.
ThugBoy takes this trope a step further. He's a Mook who'd made a successful living at getting the better of both superheroes and villains alike. Unlike a lot of these, however, he really really likes guns.
The Goddamn Maidman, who is an awesome Wholesome Crossdresser. He fights and acts like Batman...in a skirt, garters, and stiletto heels.
Ninjette could also qualify.
Colt from Femforce is the only team member who has no superpowers.
Gold Digger has a lot of them, but certainly the most prominent is Gina's mother Julia, greatest warrior of Jade Realm, who routinely takes down monstrously powerful supernatural opponents with nothing but her sword, martial arts, and her brain. In a universe where many martial artists learn to thrown chi attacks, she's one of the scariest fighters around. She even has access to magical weapons but prefers hers to be simple well-balanced blades made of spell-resistant metal.
The same goes for her rival G'nolga. Like Julia, surrounded by her team of ogres, mages, a card-carrying electric supervillain, and superstrong warriors with all kinds of weapons, compared to her dwarf with a metal-plated three section staff, she's the one you gotta worry about when the fighting starts.
The earliest Grendels all fit into this category, being only humans armed with an electrified spear who can take on Anti-Hero werewolf Argent.
In Johnny Saturn, both Johnny Saturn I and II are badass normals. Indeed, in a world full of high-powered superheroes, non-powered vigilantes are referred to as Mystery Men. Mystery men get by on martial arts, toughness, and willpower.
Judge Dredd has tangled with various supernatural enemies (including a Superman Expy), but Dredd himself is a regular human who just underwent a Training from Hell and has decades of experience patrolling the streets as a Judge, Jury, and Executioner. While Dredd himself is a clone of the first Chief Justice, the only way this really manifests is his iron will and devotion to the law. Any "superhuman" edge he does acquire is purely technologically-based, like his Department-issued Electronic Eyes or using Powered Armor from Hondo-City on a mission into the Radlands of Yi.
Mina Murray, from The League of Extraordinary Gentlemen, is the team leader by dint of her sheer force of personality. In the movie, Mina gains vampire powers, and the Badass Normal team leader mantle is handed off to Allan Quatermain. Considering that he's played by Sean Connery, it's arguably one of the few changes that works.
The muscle man Walter, the archenemy of The Mask. He's the only enemy so far to hurt Big Head and even defeated him (her). And all he needed was his large build, cunning and brute strength.
Obregon Kaine from Negation. He's a soldier trapped on a prison planet with a bunch of aliens, many of whom have incredible super powers. He wants to organize a jailbreak, but everyone hates his guts because they've become resigned to their fate and they think he's making a bad situation worse. Eventually he gets them to cooperate long enough to escape, and throughout the majority of the series, it's Kaine who holds the small group of super-powered fugitives together by being tougher, smarter and more dogged than anyone else, despite having no powers of his own.
Arwen from Sojourn, who at the beginning of the story attempts to hunt down and kill the undead Sigil-Bearer Mordath with no preparations, powers, or unusual equipment (yet). She fails, but it clearly establishes what kind of character she is, and Mordath himself compliments her skill and courage.
German comic strip detective Nick Knatterton. Once he lifts a car! (He was angry at that time; and as the author pointed out, being a taxpayer, he's used to shoulder great weights.)
In Paperinik New Adventures, Donald Duck (yes, thatDonald Duck) is this. He must use his wits and courage to fight aliens, cyborgs and the like.
Tyler in PS238 is the only student in the school who doesn't have superpowers, and has to learn to be badass very quickly just to survive. The teachers have the idea of partnering him with the Revenant, one of the new Badass Normals in this setting (he mentions that other superheroes generally feel the heroing should be left to the "special" people). To his own surprise, Tyler/"Moonshadow" turns out to be surprisingly competent; he winds up resolving situations better than most of his superpowered peers, who incorrectly believe that Moonshadow must have won theSuperpower Lottery.
Both Quantum and Woody qualify. Most notable in Woody's case, as he doesn't have the military training or combat experience Quantum has.
Amy in Sonic the Comic, she does not have the raw power of Sonic or Knuckles, but her smarts and ranged combat abilities allow her to be almost as effective in battle making her far more lethal than any other version of her to date and as well as an Adaptational Badass.
Sam and Twitch from the Spawn series. Although they don't have superpowers, they have their own skills and training to compensate such as Sam Burke's large fatty built that allowed him to fight the superhuman Udaku and vampires up close, and Twitch William's marksmanship and knowledge of trigonometry that allowed him to defeat the cyborg bulletproof killer Overt-Kill by shooting a bullet through his ear canal.
In the Infinities comic for "A New Hope," Han joins Luke in going to face both the Emperor and Darth Vader, armed with nothing but his trusty blaster. While Luke does the vast majority of the fighting, Han does manage to take down an imperial guard, and very briefly wields a saberstaff.
The comics Nomad and Rebellion centered around a mercenary named Darca Nyl, who's told to Take Up My Sword by a dying Jedi after his son is killed by a Dark Jedi the dying man was attempting to capture. During his quest for revenge, he's mistaken for a Jedi multiple times and ends up becoming a Knight Errant helping anyone he can along the way. While he lacked the Super-Reflexes of Force-sensitives, he became skilled enough to deflect blaster shots and hold his own against Dark Jedi.
The few enemies of Werewolf by Night who weren't literal monsters or sorcerers were humans like Hangman who could put a surprisingly good fight against an enraged werewolf.
Baon is Khriss' bodyguard and capable of beating up, shooting or otherwise incapacitating an entire strike team of Kerztian warrior-priests — something the entire diem of Sand Masters had problems with.
Aarik, Muggle Best Friend to Kenton, can take down Elite Mooks with two swipes of his swords, and that's when he's not trying very hard.
the military