The title character of The Fancy Adventures of Jack Cannon. One character put it best: "Jack is like the toughest guy in the universe and he will kick your nancy arse if you try anything." And just so you'll know, this was said to a freakin' Reality Warper.
It later turns out he's not so normal after all: He has Anti-Magic that gives him an edge over such reality warpers. The rest, however, is all training.
While the world of Errant Story is filled with powerful time ninja, mages, elves and other overpowered sorts running about, Jon Amraphel is just good at shooting things with a gun. While his relative lack of power is something he complains about often, it hasn't stopped him from killing or subduing many of those mentioned above with the skills he has.
Jason Chesterfield of It's Walky! is about the only character who's a normal human, and yet also among the only ones who's never had a severe mental incident. In the finale, he's gotten so annoyed with people telling him he and the human species have to wait for their god-like protector to show up, he knocks out the person who claims this, takes command, rallies everybody to fight an unstoppable extraterrestrial invasion with his commanding voice, takes control of the the conspiracy that was trying to kill him minutes before with a bit of charisma and a well-placed kick, and is the only one who isn't moved by the climax. And he never stopped being snarky.
The eponymous character of The Adventures of Dr. McNinja. Ninja status aside, when you're a (relatively) normal human that can punch Dracula in the face without flinching, you know what you are. His Sidekick Gordito on the other hand is a Badass Normal among Badass Normals, a twelve-year-old gunslinger able to hold his own among a family of ninjas. As the Doctor himself notes, he doesn't bring a twelve-year-old along for his lack of experience with girls.
The Doctor also punched out DEATH. Between that and Gordito's growing a Mustache from force of will alone, we have this trope somewhere over... Must resist obvious joke.
On the other hand, neither ninjas nor doctors are considered normal in the Dr. McNinja universe.
Airman Third Class Axel "The Unstoppable" Higgs takes the cake (unlesshe is a Jäger or otherwise augmented). He may be a nobody in the Baron's fleet without any special training, fancy gadgets, or a mysterious family past, but he's so badass that his introduction is a Crowning Moment Of Awesome.
Moloch von Zinzer is more of an Action Survivor, but he briefly ascends into badassery by having a trained (if by her own admission rather inept) ninja go wow over his survival skills.
Zeetha would also qualify (even if she is daughter of Klaus, she's neither a Spark nor construct herself).
Vespiary Squads — their job (aside of rounding up revenants) is fighting slaver wasp warriors, which is a challenge even for superhumanly strong constructs. Observe a Ruxala outnumbered by these things and "distraught". Very efficient, too.
"Commander Kickass" from Looking for Group. The first time we see him, he defeats most of the hero party by turning a table on them and disarming their caster with a thrown helmet. From all we know, he's just a standard human (or half-elf).
The main cast of characters from Faans! before they all got implanted superpowers. To start out, the only real muscle they had on their side was a quiet martial arts expert and a big bruiser. The leader was scrawny and two others had/have severe weight problems. Nevertheless, they hold their own against demigods, vampires, government agents, just plain stab-happy psychopaths, time-traveling warlords, frost giants, mental-brainwashing...the list just goes on. Granted, they did tend to grab their enemies weapons and unleash a wave of energy-blasts but that is just common sense. And the returning threat against all this is a simple rapist/cult leader. Badass normal villain. The 'Faans' make gods run in fear but this creepy bastard has scored some nasty wins.
Mob Ties has Sidney Burns who, In a World filled with cyborgs, werecats, dragons, and worse, he only needs his two fists to solve most problems. This is because he's a former soldier and a former cop. And as a soldier, he was once tortured for several months straight when he was taken captive during the war in Afghanistan/Iraq. This torture included repeated beatings, electro shock to his privates, and being forcefed gasoline to the point that it ended up giving him a stomach condition that would later allow him to breathe fire. Word of God is that Sid only managed to keep his toes during that time by using his legs to snap the neck of anyone who tried to cut them off.
Dr. Tip Wilkins of Skin Horse. He's on a team with an unkillable zombie and a genetically engineered battle-dog. Yet he's the one with the CMoA's. People keep forgetting that he was a decorated U.S. Army captain in Afghanistan, just because he's also a Wholesome Crossdresser and Kavorka Man. He rescued his teammates from a town of werewolves after being handcuffed to a bed. He stopped a rampaging clockwork mechanoid that had a nuclear weapon, and he did it with therapy puppets.
Alice of FreakAngels is an ordinary human smuggler who falls in with a group of godlike psychics. When one of them uses mind-control to rape a human girl, and nearly kills two of his superpowered bretheren, she uses her superior knowledge of the terrain to hunt him down take him out with nothing more than her trusty shotgun.
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. Despite his unwillingness to be a superhero he's usually the one who winds up getting his powered collegues out of trouble.
His mentor and Batman Expy Revenant would also count, as he relies almost completely on wits and gadgets. Revenant mentions that other superheroes generally don't like Badass Normals because they feel the heroing should be left to the special people.
Dad. He's a normal suburban businessman and the only guardian who isn't connected to Sburb in any way, and yet he kicks a ridiculous amount of ass, managing to break out of the Derse prison system because it was too much trouble keeping him locked up.
Karkat has no psychic powers, and never realized his game powers either, leaving him just an average troll with only mutant blood as a unique trait, but yet he still somehow managed to get a team of eleven others to work together and survive the game instead of all violently murdering each other, just through sheer force of will.
A bit off there — being a team leader is his game power.
That, and that he is supposedly an allegory for Troll Jesus.
Alex Rayne of the comic Wright as Rayne gets this twice. In his original identity, he's a very talented super-hero who gets by on his wits and fighting skills. When he's forced into the boy of Dorothy Wright, he's again forced to be a badass normal, but is a little miffed that he didn't get sent into the body of someone with actual powers.
Grem of the Viper Clan in Goblins has no adventurer levels like the GAP and Saves-A-Fox, nor unusual body enhancements like Dies Horribly, nor racial disposition for badassery like K'seliss, a Lizardman/Ogre hybrid. He is by all means an ordinary goblin, but he still manages to pull his own weight in battle.
Walking on Broken Glass gives us Kennedy Parker, prior to the current arc she was just an informed Badass, because a pack of werewolves respects her authority. Now in the current arc she has taken on a supernatural shadow creature with her bare hands and informed it that she will dial the pain Up to Eleven if it doesn't cooperate, which it currently is not, guess what the last two scenes of that page look like. She pulled off the barehanded Curb-Stomp Battle while a pack of transformed werewolves and a Squishy Wizard were having trouble fighting them.
Flipside introduces Bernardette by having her take out the most sorcery-boosted thug in town. It is later revealed that she does not use sorcery.
The webcomic Magellan follows a group of students at the worlds most exclusive Superhero School — the one which trains the heroes who become members of Force Magellan, the front-line defenders against the world's most dangerous threats. The main protagonist, Kaycee Jones, gains admittance to this academy with no powers whatsoever.