Elysium: Drakey and Crowe, Kruger's henchmen, who despite lacking exosuits, hold their own against Max and others, with Drakey single-handedly taking out the CCB building and forcing an evacuation.
Ash Williams of the Evil Dead series. This man only wields a Chainsaw for an arm, a double barreled Remington shotgun AKA his BOOMSTICK, a chiseled jaw, and the wit of a total jackass. Spouting off one liners left and right, this man who used to be an S-Mart clerk single handedly takes on an army of Deadites. He goes from a normal guy who is just as easily disturbed about the armies of hell as any other, to one of the most memorable movie badasses in history. Hail to the king baby.
Snake-Eyes from G.I. Joe: The Rise of Cobra (Storm Shadow is his Cobra counterpart), specificly when dealing with the Neo-Vipers. In the Paris chase he manages to do a lot more to try and stop Storm Shadow and Ana than his teammates in Powered Armor. All without having anything special besides a gun and his sword.
League Of Extraordinary Gentlemen is being run by an ordinary one - he doesn't even have Nemo's "mad science knack" for him. But seeing how it's Sean Connery, obviously he kicks as much and more ass then various immortals and Hydes.
Col. Hardy in Man of Steel. He shows no fear in fighting the Kryptonians and does his level best to kick some ass.
S.H.I.E.L.D. agents Phil Coulson, Maria Hill, Clint Barton, aka Hawkeye and Natasha Romanoff, aka Black Widow. They all serve under undisputed Badass Normal Nick Fury, director of S.H.I.E.L.D. And, if Coulson's description is accurate, the whole of SHIELD is an example.
Apart from Captain America himself, every other member of the Howling Commandos is a Badass Normal. Peggy Carter and Col. Chester Phillips from the Strategic Scientific Reserve are certainly no slouches in the badass normal department themselves, either. Special mention to Bucky, who keeps up with him for most of the film despite being normal.
Anton Vanko showed that he was capable of killing Hammer's guards with his bare hands, escaped prison without missing a beat, and while he did have a laser-whip harness, he was otherwise unprotected when he was hit by a car, a metal door, and by Iron Man himself. He stayed conscious through all of this.
In Iron Man 3 both Tony and Rhodes show they are capable of fighting supervillains without armor. In the case of Rhodes, that shouldn't be unexpected: he's a colonel, after all.
Unfortunately, this was averted in the case of Happy Hogan who confronted a supervillain and was immediately put in a coma for his troubles. He gets better in the end though.
Also, the first time Emil Blonsky faced the Hulk, he was just a soldier. He didn't fare well but was seemingly the only survivor against Hulk's rampage and certainly the only one left standing by the end of it. That says something.
Riddick of Pitch Black had this going for him until the sequel retconned him into the last of a fearless warrior race.
Sky High has Ron Wilson, Bus Driver! Until the credits, at least.
The Star Wars film series includes Jango Fett, who fights Obi-Wan and his Jedi powers using gizmos and gumption. Jango gets the worse of the combat, but his gadgets last just long enough to allow a quick escape. Later he manages to kill a distracted Jedi with some blaster sharpshooting. This must have gone to his head, because he ultimately tries to take on Mace Windu and gets rather anticlimatically curbstomped.
His clone/son Boba wasn't a weakling either. Not many people can survive being swallowed by a sarlacc threetimes or brusquely talk back to Darth Vader the way he can.
Han Solo briefly went up against Darth Vader himself and was the one who eventually killed Boba Fett (well, as far as the movies go).
Grand Moff Tarkin - for a man who cannot reflect bullets with a sword or throw lightnings from his fingertips, he is badass enough to give orders to Darth Vader himself.
Wedge Antilles - he's a normal human without the Force, but he becomes a starfighter pilot of legendary skill, founding the elite Rogue Squadron and achieving feats on par with the greatest jedi pilots. He also is the only person to fly a starfighter during both Death Star battles and survive.
The Transformers Film Series has an interesting example of how a group of characters grow into the role of Badass Normal. When they start off human soldiers were completely helpless against the Decepticons, as they would shrug off .50 cal machine guns and anything lower with no problem. Lennox and Epps managed to discover (almost by accident) that they were vulnerable to HEAT (High Explosive Anti-Tank) rounds, which they fired from hand-held weapons, as well as the reallyheavy weapons fired from artillery platforms. But due to difficulties mobilizing support crafts and hand-held weaponry not capable of extensive enough damage, they were still relying heavily on Autobot support during the course of ROTF. By DOTM you see soldiers training directly with Autobots in how common infantry soldiers can do real damage against the big robots: using trip wires, blinding them with parachutes or sniper rounds, planting grenades on their feet to disable them... using Badass Normal strategies over heavy firepower. In the final battle of DOTM it effectively becomes Bash Brothers with equal footing with the Autobots and Human Soldiers just decimating the Decepticon ranks.
In the X-Men films, the average cop or soldier is capable of fighting against mutants. They might not always win but they put up a fight.
The military is Genre Savvy enough to go after Magneto with non-metal weapons and took out quite a few members of his mutant army before the X-Men showed up to lend a hand.
A random security guard was the one eventually took down Mystique.
One cop briefly took Wolverine down with a shot to the head.
In X-Men Origins: Wolverine, Stryker was the one responsible for shooting Logan in the head with an adamantium bullet, giving him amnesia.
The Wolverine: Harada, Shingen, the latter who easily defeats Yukio and fights Wolverine, inflicting several instantly lethal wounds that only his healing factor allows Wolverine to win, Yukio, even the Yakuza who serve Shingen Yashida are pretty damn tough and impressive fighters, even when pitted against Wolverine(we get to see Wolverine go toe to toe with two Yakuza who end up on the roof of a bullet train with him. The Yakuza that Wolverine fights manages to hold onto the tanto he's attacking Wolverine with, use it to anchor himself to the roof, and leap up to dodge any oncoming obstacles and survive the fall back down onto the roof of the bullet train).
A unusual example of this occurs in Spider-Man 2, where the citizens on the train that Spider-Man just saved see him with his mask off and realize that, despite having super-powers, the "guy behind the mask" is actually just a normal human teenager, who presumably goes to school, and has a normal life like every other teen. Although unacknowledged, it's this fact that makes them all stand up to Doc Oak, to try and protect Spidey. Who just uses his "robotic arms" to move them out the way.