Mighty Lumberjack

Joseph Montferrand, the Real Life person who inspired the creation of the Ur Example "Big Joe Mufferaw"

"In a period of industrial development and modernization in urban areas, logging remained a traditional business in which the workers exhibited pride in their craft, their physical strength and masculinity, and guarded their individualism. Their camps were a bastion of the traditional workplace as they defied modern rationalized management, and built a culture around masculinity."

—The Other Wiki, "Lumberjack"

Lumberjacks are commonly used to represent strength, man's dominance over nature, and the idea that axes are pretty cool. In fiction they tend to be Badass, often to the point of Testosterone Poisoning. Either that, or to sell paper towels.

Because people will expect a lumberjack to be manly, they are almost always men. They tend to dress like a stereotypical 19th century Paul Bunyan type with a flannel shirt, rugged outdoorsman look, a Badass Beard, and large muscles developed from years of swinging an axe. Often a Big Eater, as such hard work makes a guy hungry. The much rarer female lumberjack will either be a Butch Lesbian and Played for Laughs, or look exactly like a normal girl wielding a giant axe, with her lumberjack heritage used to Hand Wave her insane Super Strength.

Examples of Mighty Lumberjack include:

Advertising

The Brawny Paper Towel company tries to link this trope to the strength of their product by making their mascot a giant lumberjack.

Film

Invoked in Hoodwinked with Kirk the Woodsman, an actor playing a burly German axeman in commercials.
In X-Men Origins: Wolverine, lumberjacking is what Logan does in his Retired Badass phase.

Literature

The God Box by Barry B. Longyear features a female lumberjack (who happens to be a fifteen-foot tall giantess).
The Tin Woodsman in the The Land of Oz books. A pretty decent fellow, but when his allies are in danger he can "fight like a Roman gladiator", as one book claims, proven in the first book when the Witch sends her savage pack of wolves after Dorothy and her friends and he hacks them all to death, by himself.

Live-Action TV

Full House: One character spent some time hosting a children's television show and invited a second character to join it. The latter man scoffed at the idea, thinking it below him, till he was offered a role whose manliness satisfied him: "Lumberjack Jess."
Malcolm in the Middle played with this for a while, with Francis and his friend from military school believing they would be able to run off to Alaska and become these relatively easily.
Flirted with and then subverted in the Monty Python's Flying Circus Lumberjack Sketch. The singer dreams of being a lumberjack ... and Camp Gay at the same time.

Music

"The Haircut Song" by Ray Stevens is about a variety of haircuts Stevens has received from insane barbers. Whenever he is feeling intimidated by a barber and is asked what he does for a living, his immediate response is "I'm a logger!":

Now a lot of people would be intimidated in a situation like this...I was not. I am what I am, play my piano, and sing my little songs. I looked him right in the eye and I said, "I'm a logger - just up from Coos Bay, Oregon. Been toppin' trees - quite possibly the toughest man in the entire world."

"The Lumberjack Song" from Monty Python's Flying Circus. Lumberjacks are given the same treatment in that song as Arthurian Myths were given in Monty Python and the Holy Grail.

Oral Tradition, Folklore, Myths and Legends

Paul Bunyan is the ~~Ur Example~~ Trope Codifier, having originated in Canada in the early 19th century. There are many myths surrounding him, the most famous of which is that the 10,000 Lakes of Minnesota were formed by him and his sidekick, Babe the Blue Ox, as they walked around in a blizzard. It's worth noting that most of the Paul Bunyan myth, including everything about Paul being a giant with a giant pet ox, was actually the invention of a 20th century copywriter who spun Paul Bunyan into a mascot for a logging company.
The Ur Example is Big Joe Mufferaw, based on real-life lumberjack Joseph Montferrand. Some of the stories about Big Joe Mufferaw would later be re-told with Paul Bunyan taking his place.

Video Games

Kingdom of Loathing: In Little Canadia, the player can encounter lumberjacks, lumberjills, and lumberjuans. The lumberjack supervisor carries two double-sides axes.
In Princess Maker 2, being a lumberjack increases your strength, which increases your attack power, which means if you do it enough, you'll be be killing enemies in one hit.
Tales of Symphonia: Presea Combatir is a female lumberjack. She looks about twelve years old but carries an axe bigger than some of your other party members.
In the computer "card" game Urban Rivals, the first boss card you get in your collection is a lumberjack. He starts looking like the stereotype and hulks out when levelling up. Also adds bonus damage to the whole team.
Bear Hugger from Punch Out is an atypical Canadian lumberjack who moonlights as a boxer.

Web Comics

In The Adventures of Dr. McNinja, lumberjacking makes people susceptible to Paul Bunyan's Disease, which causes those it affects to turn into a giant lumberjack who is "enraged at how many trees still stand within his vicinity."

Western Animation

In the The Simpsons episode "The Blunder Years", Marge becomes infatuated with the lumberjack that is the mascot for a brand of paper towels.
In Gravity Falls, Wendy Corduroy's father is a really tough lumberjack named Manly Dan. They don't call him that for nothing.
The Smurfs had one-shot character Timber Smurf. He was as tough as Hefty with an appetite to match Greedy's.