Then there's Michael the archangel, patron saint of police officers, military, mariners, paratroopers, EMTs, the Greek Air Force, knights, swordsmiths and grocers.
It's said Satan and his various minions greatly fear Mother Mary. The rosary is the strongest weapon a prayerful person has in their arsenal.
David slew Goliath with a pebble and a slingshot (actually easier than it sounds).
Buddhism: Guan Yin. Seriously, he/she's probably the most insanely awesome depiction of a badass pacifist to have ever existed.
Taken literally in M.U.G.E.N, where she works like the F1 button, but on steroids. By that, we mean she can take down nearly any character, even god-tiered ones such as Chuck Norris. There have been several versions of her, with varying cheapness for each version.
French-Canadian lumberjack Joseph Montferrand (1802-1864), known in English as "Big Joe Mufferaw", is a legend in the Ottawa Valley for his strength and skill. (The court house in Gatineau, Quebec, is named after him.) Two verifiable stories are that he knocked out the boxing champion of Canada with one blow in a fight and that one night he single-handedly beat up as many as 150 Irishmen who ambushed him on the Chaudiï¿½res bridge. Subsequent stories (and a song by Stompin' Tom Connors) attribute such feats as putting out a forest fire between Arnprior and Renfrew while in Smiths' Falls (38 miles away) by spitting at it, and driving a log raft down the rapids-strewn Ottawa River from Mattawa to Ottawa (a distance of over 250 miles) in a single day.
Most American Tall Tale characters started as either Real Life people or mildly exaggerated fictional characters. Then people got to exaggerating them, then those exaggerations got exaggerated, and so on and so on. And, since they're Public Domain Characters, those exaggerations eventually become Canon.
Davy Crockett used to kill a hundred bears each morning for breakfast, then go and kill a few dozen panthers for a snack. He could wrestle comets, wade the Mississippi, whip his weight in wildcats, stare most any critter to death, and shoot a baby gnat from two hundred miles on a foggy day with his eyes closed and holding his rifle with his feet.
Oh, and make a coon-skin cap look good.
The Real Life Davy Crockett was no slouch either. He was indeed a noted frontiersman, but perhaps his truest display of badassery was during his career in the House of Representatives, when he defended the rights of Native Americans at a time when President Jackson was illegally seizing their lands. Crockett condemned the President for his actions and refused to back down from his defense of the Native Americans. That's right folks, Davy Crockett was tough enough to stand up to Andrew Jackson and fought against a racist practice as early as the 1820's. When asked about why he didn't back down and go along with the President, Crockett replied "I bark at no man's bid. I will never come and go, and fetch and carry, at the whistle of the great man in the White House no matter who he is."
John Henry gave his life to prove his—and by extension everyone's—awesomeness.
In Classical Mythology Hercules...uh...Heracles...uh...Herakles remains one of these even to this day. In myths he was often presented as the World's Strongest Man, defeating, among other foes, death himself on behalf of one of his friends and is commonly held as having invented wrestling as a formal sport. His name has entered into the English language as a byword for incredible feats of strength.
Cu Chulainn will FUCK YOUR SHIT UP. In the battle he died in he tied himself to a rock with his own intestines so he could remain upright and continue fighting.
King Arthur. Depending on the Writer. While he tended to get eclipsed by his Knights of the Round Table (especially Lancelot) as the Arthurian legends developed, in the early stages he was fighting monsters like the Giant of St. Michael's Mount and once single-handedly killed 960 men in a battle. When people like Sir Thomas Malory were compiling single narratives out of the many legends, these incidents were relegated to his younger days.
There is no doubt at all that the original Welsh tradition about Arthur featured him as this. He had the nickname the. Red Ravager of Britain and he did all his own dirty work originally. In fact, the earliest mention of him uses him as a measuring stick for other badasses. And they're all found wanting.
Norse Mythology is chock full of these, but of course the most well known, and therefore memetic, would have to be Odin and Thor.
In one story, Thor, Loki and Thjalfi (a farmer's son and servant to Thor) visit the halls of the giant king Utgard-Loki. Tricked by Utgard-Loki's illusions, Loki nearly wins an eating contest against fire, Thjalfi holds his own in a race against thought, Thor hits the ground so hard with his hammer that he creates a series of hills, drinks so deeply of the sea that he creates the tides, lifts the body of the serpent who encircles the world from the ground, and wrestles well against old age. Utgard-Loki is so terrified that he banishes Thor from his lands and vanishes.
And on that note, for a non-god version of this, Ragnar Lodbrok takes the cake.
Kintaro, from Japanese folklore, who would supposedly sumo-wrestle with bears as a kid.