Many of the veteran crimefighters of Astro City are regular folks coupled with a few gimmicks (Jack-In-the-Box, Crackerjack, Altar Boy), but who have trained their reflexes up to bullet-dodging levels. It gets 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.
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.
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.
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.)
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.
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 Star Wars "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 dual bladed lightsaber.
Every single hero or villain in Watchmen except Dr. Manhattan, the only being in the universe with super powers, and Ozymandius, who doesn't have superpowers but does have sufficiently advanced technology to replicate them (genetically engineering telepathic alien squid, for instance).
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.