Eric from Blizzard Storm definitely fits this trope, as he is able to go up against Angels and Demons and win.
Child of the Storm has Clint Barton, Natasha Romanova (to an extent) and Carol Danvers prior to her super soldier heritage being activated and her temporarily becoming the new Green Lantern), every single one of whom can kick all of the ass without explicit superpowers.
Uhtred is this by Asgardian standards, to the point where Sif picked him out to be her protégé.
BlackDragon6's Ranma ˝ story Guardian features a character named Ken "Snake" Yakata, a Jewish gun nut who is routinely billed as the most deadly fighter in the Department of Abnormal Phenomenae Containment with the sole exception of Ranma. This is in spite of the fact his other officers are: a powerful psychic psycho capable of cutting the heads off powerful vampires, a superhuman capable of going toe to toe with cyborgs and the worst boss enemies in the Resident Evil series, and a bloody Zergling. All Snake has is a shotgun. And lots and lots of firepower. (The man somehow have a working ICBM silo in his house)
To further emphasize the extent of this, it should be mentioned that Snake terrifies every single one of his fellow officers, save Ranma. To an extent, anyway. They know he can't shoot them and thus they feel somewhat secure around him, but around his evil clones they are terrified.
In the spin off Millenium, during one encounter, the DAPC's captain have a threat index of 5 while the Sailor Senshi got a 4 .Snake? A solid 10.
Last Child of Krypton: Kaji, AKA Batman. In a world where teenagers pilot giant robots and have super-strength, super-speed, invulnerability or can create energy constructs using their willpower, he is a completely normal human who is skillful enough to beat super-powered adversaries.
Jason Shepard of Sailor Moon: Legends of Lightstorm has become this due to an unknown event that made him lose his status as Lightstorm. Although his body retains some of its properties, such as agelessness, his powers are gone. Technically, his loss of transformations has given him the ability to unleash a small burst of stinging energy, but this is a result of his transformations malfunctioning, rather than an actual power. For all intents and purposes, his body is human but that hasn't stopped him from being one of the deadliest men alive. He has been seen to fend off multiple Negaverse drones with his staff, grapple gauntlets, and explosive shuriken. His pain tolerance is legendary, and he has consistently been seen to stand up to even the toughest of Negaverse enemies, including a two-bodied Zoisite. In fact, his skill is so great that considers slaughtering entire squadrons of humans armed with rifles to be "training".
Balian of Ibelin in The Chance Encounter series. While he has been rendered immortal, this only seems to prevent him falling ill or indeed ageing. He also fights alongside Achilles, Legolas and Will Turner (during his "undead captain of the Flying Dutchman" period) and holds his own easily. When he is briefly turned evil by dark magic, he even forces LEGOLAS into retreat. He also takes on many of King Richard I's soldiers at once and wins, with the King's spymaster not sure if the King (who was a noted warrior himself) would survive a head to head confrontation. Oh yes, and he wades through HELL ITSELF to save his dead-by-suicide wife, taking on Satan and...mostly getting the crap beaten out of him actually, but he stood up to the ultimate evil and survived!
Author Avatar Art of the Mass Effect self-insert Mass Vexations eventually becomes a good Soldier-class unit within Shepard's squad. He never got any of the genetic implants that most soldier-class units get in the Mass Effect universe. He also Took a Level in Badass considering he had never fired a gun in his life before entering the Mass Effect universe.
In the Transformers fic, They Just Don't Care Anymore, the character Alien spends a lot of time being criticized as a minor character who won't get to do anything important and will inevitably be the first to die when a horde of undead attacks... until a horde of undead actually attacks. In a Moment of Awesome, she announces that she's sick of being called a minor character, whips out a pair of kukris and single handedly takes down everything in her path, after which she proceeds to throw a guy into a quarry because he annoyed her.
Poké Wars has Samurai, a Pokémon trainer who lost his Pokémon early on in the war. Yet, he is more than capable of holding his own in a fight against them with only his katana.
Lt. Surge also counts. He was able to hold off a group of Electivire and Scizor with only a combat knife.
Don't forget Tracy. He held off pokemon from Oak's ranch with nothing but a lead pipe and sleep deprivation.
Gwenith Cousland and Theron Mahariel in the Dragon Age fanfiction Dragon Age: The Crown of Thorns qualify, although the latter's very sharp hearing could be seen as a Charles Atlas Superpower in its own right. Of course, seeing as how everyone else, especially Kallian Tabris, either came with or gained some power or another over the course of the story, it is unclear if this status will last for the human noble and Dalish. Leliana and Zevran still fit perfectly though,
A few in Spider-Man Evolution, most notably Daredevil and Moon Knight, both being able to kick Spidey and Black Cat's butts without the use of powers. Similarly, both Kraven and Silvermane, both completely normal people in this story (the latter being past his prime as it is) and are capable of tossing Spidey around when they faced him the first time around. Both MJ and Detective George Stacy are also notable during Chameleon's hotage takeover, MJ basically goes around knocking out mooks with a frying pan and ends up saving the day, while George Stacy beats up an armed mook who threatened his daughter without any weapon himself.
Alex from Adventure Time fanfic, Alex. She's a nerdy human girl who acts as Marceline's opponent in the election for the position of Vampire Queen. Despite that, she can take on the Vampire Queen herself with her laser pistol and lightsaber, as well as her blocking skills.
The Pony POV Series has several, but the one that stands out the best is Patch from the 7 Dreams/Nightmares Gaiden story. After she Took a Level in Badass in her quest for the Shards of the Rainbow of Light, she becomes an Action Mare capable of taking on a full grown dragon and freaking Grogar by herself and winning. The only 'superpower' she has is an extremely slow aging process caused by the Shards. Besides that she uses guns, and when those die out, a sword.
Hermione's parents, of all people in Knowledge is Power. They may be Muggles, but they're deadly with firearms.
In The World of the Creatures, Brendan Anderson is just your average, 19 year old English Major. And yet, through his combination of heart and smarts, he's able to stand toe to toe with the likes of Buffy Summers, Batman, and the Doctor.
Equestrias First Human: Connor, the human who ends up in Equestria is beat up by a pair of traitorous royal guards, and still has the strength to take down a ragtag group of rebels with makeshift weapons alongside Spike, and then he overpowers and defeats Hellfire-the Big Bad and a deranged unicorn stallion powerful enough to slay a dragon- singlehandly.
In the sequels, he still qualifies as an Earth Pony, an example being able to survive a battle with Queen Chrysalis who at that point was strong enough to defeat Princess Celestia.
The protagonist of Middle Of Nowhere arrives in Fereldan as a middle-aged and dinged up Army sergeant. He relies on his wits and only just survives his first encounter with some live darkspawn, but levels up over the course of the story. Still, he does lament not being "an all-powerful mage."
Rarity starts off as captain of the school Judo club, and is shown to be more than capable of kicking ass even before becoming a mahoushoujo.
Likewise Applejack, who is a powerhouse even before joining the team. Best shown when she mows down large numbers of the Infestation swarm with just her fists and some Improvised Weapons.
Lightning Dust is a villainous example. In a setting full of demonic monsters, magic users, and ninjas, all she's got is some Le Parkour skills. And she's still able to hold her own against the mahoushoujo.
General Ty Jun from Kyoshi Rising; the man who invented Chi Blocking. He is the only Non-Bender who has ever faced Avatar Kuruk in a fight and won, and routinely trounces Kyoshi in their sparring matches.
Dark Action Girl Charisma despite being literally born with what is essentially a Blood Knight cutie-mark, is just a normal, if mentally unbalanced pegasus, who's only unique ability is her "talent" constantly telling her the best ways to kill anypony in her immediate area. Yet, she is so badass she used train griffins and is more then capable of handling enemies several times her size and strong enough to kill her in one blow. She is so feared that she even earned herself the nickname "The Ass Kicker" and is said to be invincible in a fair fight. It really says something, that in a cast of heroes consisting of a skilled magic user, resurrected heroes who are far stronger than modern ponies, a griffon, and dragon, they still have to fight dirty to beat her.
Though not as big an example as the above, Detective Hard Boiled, who despite having a degenerating condition that seriously weakens his magic and no unique powers directly relating to combat, manages to keep up with the other and take out Mooks just through intuition and police training.