The Batman mythos tends to collect these. Most notably, of course, being Batman himself. He fills this role when he's required to be in an ensemble. Despite having no inherent superpowers, he's earned a spot in the inner circle of the Justice League of America, fighting alongside the likes of Superman courtesy of a steel-trap intellect combined with a bit of a mean streak that means he can consider plans other members can't, and consider them well. Batman has the proven ability to develop the means to disable each of his fellow Leaguers — proven when those plans were stolen by villains and used to great effect.
Honestly, Batman's Badass Normal status is cemented by the fact that several high-profile beings (including the above mentioned Spectre and Superman) have such high regard for a "mere mortal". Harbinger once referred to him as "the Scourge of all Evil."
Nightwing (the original Robin's adult superhero identity) is likewise unpowered and is on par with Batman in most of Batman's skills. He surpasses him in leadership ability: he's about the only person in the world that every superhero would listen to without question. Nightwing actually became Batman for a time, so it comes full circle.
Cassandra Cain (the 3rd Batgirl). Through physical conditioning alone, she can perfectly read body language and anticipate her opponent's next move. She's been trained by Batman, and is arguably a superior fighter, having beaten the best martial artist in the DC Universe, Lady Shiva.
The Joker is essentially this. In most portrayals, he doesn't actually have any powers, but he's still fully capable of going toe-to-toe with any superhero in The DCU, including Superman and Wonder Woman, and often will come very close to beating them.
Two-Face, a man with his face (and mind) split in half, armed only with guns and a coin that often spells trouble for those that happen to end up on its bad side, Batman especially.
The Penguin, a short, stub of a man and one of the most dangerous mob bosses in Gotham City's underworld. He's often triumphed over Batman with just a trick umbrella.
The Riddler, who usually doesn't even meet the Dark Knight face-to-face before defeating him with his incredibly high intelligence and perchance for traps and brain-twisters.
Minor Batman villain Catman used to be a walking joke, but now he's an incredibly dangerous mercenary for hire who lived with a pride of lions.
The top guard in Arkham Asylum, Aaron Cash, is a tough-as-nails and brutal man, often using extreme force to keep the inmates in line. Don't get the wrong idea, though: he's also a noble man with a good heart and moral compass. He's ruthless because he's outnumbered by the most sadistic, evil, and insane people in Gotham, and he and the other guards are the only thing keeping them from terrorizing the city. So what makes him a Badass is that he does manage to keep control of them. He's a man who will go toe-to-toe with the Joker, Two-Face, Zsasz, and Killer Croc (until the accident...) without a moment's hesitation. Shame they essentially made him a tough talking damsel in distress in Arkham Asylum and Arkham City...
Superman's Arch-EnemyLex Luthor glides under the radar on this one, but gets his due from time to time. Superman: Red Son outlines his whole get-up rather neatly: "What was the point of Lex Luthor? A human who dared challenge a god, surely he was the greatest of his kind."
Post-Crisis Lois Lane as well. A few abilities are due to her exposure to a lot of weapons and physical skills while growing up on military bases and all, but for the most part it's just that she apparently has cojones the size of Metropolis. Who has the luxury of being incinerated by that alien overlord or getting gunned down by a gang of mob members when you promised Perry White you'd get back to the Daily Planet with a front-page story before 8:00?
Played with in the case of Clark Kent. Yeah, sure, he's actually Superman, but to the world at large Clark Kent is just a mild mannered reporter who dares to muckrake around Lexcorp and Intergang. In the One Year Later arc, Clark actually loses his powers for a period of time and still manages to infiltrate Lex's operations, Intergang, and anywhere else you'd expect an intrepid investigative reporter to go. And, according to Perry White, is a BETTER reporter that year than he's ever been. Apparently Clark Kent is just plain badass.
The Green Arrow family (Green Arrow, Green Arrow II, Red Arrow, and Speedy) are all unpowered. Improbable Aiming Skills and Trick Arrows aside, Green Arrow II is one of the best martial artists in the world, Speedy is an HIV-positive superheroine, Red Arrow is the fastest archer in the world, and GA himself is mostly a being of pure, unbridled moxie. He's one of the few people that are completely unafraid of Batman.
Considering that Green Arrow was originally conceived as a Captain Ersatz for Batman, this isn't surprising.
Everyone in Jaime Reyes' supporting cast that doesn't have superpowers, especially Brenda and Paco, aka Anger Girl and Stick Boy. And Jaime's predecessor Ted Kord.
One issue of Superman, pastiching the Silver Age, had a story where practically everyone in Metropolis gained superpowers identical to Superman's, going so far as to don capes and costumes (and Superman himself having to don a rather tacky costume while still masquerading as Clark Kent) and the mayor proposing the city name be changed to Superpolis. Then Metallo shows up and exposes everyone to his kryptonite, and they start dying from it like Superman would... until Detective Dan Turpin (who appeared earlier and disparaged Superman over how real crime fighters don't need superpowers), dressed in normal clothes, walks out of the crowd, unaffected, and arrests Metallo and saves everyone. It turns out the whole situation was set up by Mr. Mxyzptlk to give everyone superpowers - along with a kryptonite weakness - but since the detective wholeheartedly didn't want to get powers, he didn't get kryptonite vulnerability either. Then he gives Mxyzptlk a note to read, tricking him into banishing himself to the fifth dimension again. In other words, several dozen superpowered people lay around gasping for breath while a portly detective in a bowler hat outwitted two major villains.
Dan "Terrible" Turpin is that badass in every adaptation, especially Superman: The Animated Series where he stood toe-to-toe with Darkseid and didn't blink. It cost him his life, but he knew that going into it and still stood up to the Man.
His original Crowning Moment Of Awesome, back in the original New Gods, was attacking Kalibak with nothing but a tommy gun and getting mauled within an inch of his life—all to keep Kalibak distracted until he could be fried with all the electrical power in Metropolis, knocking him outó so the son of Darkseid, god of evil, could be arrested.
Any human Green Lantern, deprived of his/her ring, becomes this by default.
This is helped by the fact that two of them (Hal Jordan and John Stewart) either serve in or have served in the armed forces.
In the relaunched Green Lantern, Hal jumped out a window to reach the building across from his where a woman was being domestically abused. Later he got a weaker copy of the ring. He proceeded to outrun a planet of super-villains with nothing but a ring powered motorcycle.
Many Green Lanterns, though aliens, don't tend to have abilities that would be considered superhuman. Sinestro without his ring is still able to put up a decent fight against both Hal and John (both similarly depowered).
In every Legion of Super-Heroes continuity, Val Amorr, Karate Kid, is the one member of the team without superpowers. However, his skill with martial arts is such that he can fight Superboy to a standstill — you tell him he's not good enough for the Legion.
Quite a few of the members of the Justice Society of America fall under this, however, there are some notable examples. There's both iterations of Mr. Terrific (Terry Sloane and Michael Holt) who exemplify Charles Atlas Superpower as Olympic-level athletes with multiple PhDs (Holt has the distinction of being the third smartest man in the DCU). And then there's Wildcat who has no superpower beyond a prize-winning right hook. Oh, there's also a case of a weird backfired magical curse that gave him nine lives, but the fact that comes up so rarely is a testament to how good he is at what he does. And what he does is punch people.
In the Marvel Universe, Hawkeye has no powers, just a bow. And, when alien invaders summon a zombie army to destroy the universe, guess who is one of the only two people standing at the end of it. Go on, guess. Not bad for "an orphan raised by carnies, fighting with a stick and a string from the paleolithic era."
Plus Hawkeye II (also known as Golden Archer, Wyatt McDonald of Squadron Supreme) and Hawkeye III (Kate Bishop, jokingly called "Hawkingbird"). The latter's first appearance in the Young Avengers, all either superpowered or having fantabulous armor, involves her saving the team's bacon during a botched hostage situation, later to become the official "Bad Ass" member of the team.
Mockingbird — an intelligence officer who fights crime with nothing but two staves and the flexibility of a gymnast. She later got upgraded to Empowered Badass Normal (that happens alot in Marvel).
"I may not have the claws and the webs... but I know a thing or two about a thing or two. Yeah, that's right... run like a bitch."
Ben Grimm, aka the Thing, is clearly not normal, but sometimes in the history of the Fantastic Four, Reed or someone else has managed to cure him and restore him to human form, although such cures are always temporary. During these times, Ben certainly fits the description, often able to fight alongside the team with nothing more than what he learned in the Yancy Street Gang.
Bucky Barnes, prior to the cybernetic arm and becoming Winter Soldier.
Black Widow: "world class athlete and gymnast, expert martial artist (including karate, judo, aikido, savate, various styles of kung fu, and boxing), markswoman, and weapons specialist as well as having extensive espionage training. She is also an accomplished ballerina." says Dr Wiki.
Almost every Daredevil villain. The (non-female) Bullseye started out as a professional baseball pitcher who somehow developed enough skill to turn anything he got his hands (or feet, or teeth) on into a lethal throwing weapon. While
The Punisher has no superpowers, but more than makes up for it with deadly martial arts skills, a brilliant tactical mind, and enough firepower to destroy a country. The skills of both the Punisher and Captain America are such that they've repeatedly tangled with superhuman foes and come out ahead by using their skills in clever and creative ways. (The MAX (mature readers) Punisher story Born may subvert this by implying that he may have made a deal with the Grim Reaper to continue to live in order to keep killing, but it is the only such hint in all of MAX Punisher. Otherwise, he's just a Badass Normal who looks his age and has been confined to bed rest multiple times from severe injuries.)
Similarly, Marvel Comics' Kingpin uses both his powerful brains and more powerful brawn to keep the costumed villains in their place, and screw over the heroes. Oddly enough, he started off as a Spider-Man villain where it was specifically stated that he had superstrength, the origin of which, was a mystery. It was to the point where it was all but stated he was stronger than Spidey who can lift roughly 10 tons. Once he shifted over to a Daredevil villain, he had a Retcon, explaining that he was just a really strong human. After that, whenever Kingpin showed up in Spidey comics, he curiously turned into a master-manipulator type instead of the brawler he once was.
Alex Wilder, from Runaways, who's also team leader. It turns out he's The Mole, but that in no way reduces the badassitude of his actions.
Chase Stein, despite being considered the least intelligent of the group, has street smarts enough to figure out how to outwit the Gibborim while he also forcibly recruits the geek squad who worked for Wilder Senior.
Alex's father, GeoffreyWilder, is a villainous example in both his 1985 and 2000s incarnations. He's been the leader of The Pride (a group that includes Mad Scientists, aliens with Light Is Not Good powers, time-travelling criminals, Evil Sorcerers and Mutants) since day one on the force of personality alone, and took control of most of LA, while the rest of The Pride handled out of town affairs. When his 1985 incarnation is brought to the future he proceeds to give the Runaways a serious fight, ultimately kidnapping Molly and killing Gert before being banished back to his own time.
Also in the MU, Storm of the X-Men lost her powers for some time, made do as a Badass Normal, and still proved a great field leader of the team, beating out the powered Cyclops for the leadership position (although Cyclops was mentally influenced into losing by Madelyne Pryor). It even proved an advantage at one time, when the team was trying to stop the infamous massacre of the Morlocks. During that battle, a villain who could neutralize powers with his touch tried to do so with Storm, but she had no powers to affect and he left himself wide open for a knockout punch by her to put him out of action. She's also taken out Callisto and Crimson Commando in hand-to-hand combat, both of whose mutations make them nearly superhuman fighters, and she did so without using her powers.
Iron Man's buddy Rhodey was also this before he became War Machine. On the villainous end of things we have Mark Scarlotti, alias Whiplash I and Blacklash I, who, for forty years of publishing history, fought Iron Man armed only with a kevlar bodysuit and a pair of titanium whips.
Rictor, after losing his powers during House of M/Decimation, has turned into this. Peter David describes him as the "moody former mutant who believes heís useless and yet keeps happening to save the day." He's saved Siryn from a kidnapper, beaten the Isolationist and Arcade, programmed Danger Room technology to create a very convincing illusion, and helped stop Quicksilver from blowing up any more former mutants.
The Evil AlbinoSpider-Man villain Tombstone originally had no powers, and was, in Spidey's words, "Just a guy." He was just a guy with a tendency to Neck Lift people while strangling them to death — one-handed. When he and Spider-Man finally fought after a several-issue storyline, Tombstone gave the overconfident superhero a No-Holds-Barred Beatdown at first using just his hands and then a metal pipe. Once Spidey realized that he was actually dangerous, he got serious and served up a Curb-Stomp Battle to the mob enforcer. Eventually he crossed over to become a Empowered Badass Normal with brick powers after his old "friend" Robbie Robertson trapped him in an airtight chamber filled with gaseous Applied Phlebotinum.
The character "MVP" manages to become the best human possible, by various exercise programs and diets. Yes, he ate his veggies and did his pushups in just the right combination and everyone thought he had superpowers.
Wolverine foe Shingen Harada, a Yakuza boss with no superpowers who, despite his advanced age nearly killed Wolverine in the seventies.
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.
ThugBoy from Adam Warren's Empowered 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.
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.
Most of the heroes in Watchmen lack superpowers (the exception would be Dr. Manhattan) and yet are extraordinarily skilled fighters.
Manhattan is actually an inversion.
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.)
Both Quantum and Woody qualify. Most notable in Woody's case, as he doesn't have the military training or combat experience Quantum has.
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.
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.
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.