Played for laughs in Code Geass. Lelouch may be a Magnificent BastardChessmaster who can single-handedly win a battle thanks to his strategy... but when stuck in the wilderness, he attempts to dig a deadfall in order to catch an animal...and exhausts himself before it's even two feet deep. He's forced him to eat the fruits his half-sister Euphemia found with an embarrassed expression on his face the whole time. This ties in with his being a Non-Action Guy. In contrast, his much more athletic friend-slash-rival Suzaku is shown fishing bare-handed and produces more than enough food for himself and Kallen.
In The Walking Dead, the tougher men are more rural and know how to do things like hunt and track. More urban men like Glenn are wimpier.
Brought to an infamous extreme in Deliverance, where only by going back to their "primal" selves were they able to last.
The men in Fight Club fight as a means of returning to their primal nature instead of living in an emasculating consumer culture.
Subverted in the 1964 film Man's Favorite Sport? wherein Rock Hudson plays a fishing expert at Abercrombie and Fitch (this was back in the days when it was still just a world famous outdoor sports emporium) who can't fish. Entered into a fishing tournament by a publicity agent who doesn't know his secret, Hudson is forced to hire an Indian guide to catch his fish for him. And, yes, fishing is not the same as hunting, but it is the principle that counts.
This trope is a central element of Ernest Hemingway's "Short Happy Life of Francis Macomber," in which the wealthy title character takes his wife on a hunting trip and finds himself upstaged by the hunting guide, Robert Wilson. Macomber struggles to prove himself a competent hunter as his wife flirts openly with the more confident and masculine Wilson: he eventually succeeds in shooting a buffalo, but shortly after he is shot by his own wife. Hemingway leaves it open whether this second shooting is accidental or intentional.
Robert A. Heinleindefied this trope in one novel by having a character note: "A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects". Note that this is Human Humans, not just Manly Men.
Subverted in Romance of the Three Kingdoms: When the emperor announces a royal hunt, Cao Pi has all of his quarries captured alive and is praised for his mercy.
Played straight by Rudyard Kipling in the Jungle Books, if you count anthromorphic wolves as "men".
Robert Baratheon in A Song of Ice and Fire is a warrior king who is shown constantly whoring, drinking, and hunting. A combination of the last two are what get him killed; the first is what sets up much of the plot.
Live Action TV
Supernatural. Obviously Sam and Dean share a background, and they both "hunt" (demons) but manly Dean who accepts his blue-collar roots can not merely fix but rebuild cars, while Sam who went to college and wanted to be a lawyer (and whose masculinity Dean likes to make fun of) isn't allowed to drive any more and does not know how to do anything similar.
Arthur from Merlin goes hunting all the time. Two episodes revolve entirely around his fondness for the sport. Interestingly, the show does not necessarily approve of his hobby, as many of his hunting expeditions end in disaster, and Merlin, the studious wizard, explicitly states that he does not like the sport. It's a Sensitive Guy and Manly Man contrast.
On That '70s Show Red takes Eric hunting, then berates him for half of the episode when Eric misses a shot at a buck at close range. Eventually Eric reveals that he's a great shot and missed because he didn't want to kill the buck; interestingly, Red says that he can respect that a lot more than Eric just being a lousy shot.
Like his Literature version, Robert Baratheon in Game of Thrones is an enthusiastic hunter. His wife Cersi claims this was his way of avoiding having to deal with his family.
Cersi: Whenever I came close to bringing a baby into the world, Robert would run off into the woods to hunt. On his return, I would present him with a child. He would present me with the head of some dead beast.
In one Klingon province, courtship begins with the man presenting a leg of freshly killed meat on the woman's table.
Subverted in Hannibal. Profiler Will Graham lives alone with a pack of dogs in a rural area, where he fishes, crafts his own lures, and fixes boat motors. However, he lives in isolation mostly because he's so sensitive to other people's emotions that he finds too much human interaction overwhelming, and he's easily dominated by his urbane, culture-loving, Supreme Chef aesthete of a psychiatrist... Hannibal Lecter. Funnily enough, Hannibal is great at hunting too.
In the tie-in webcomics for Heroes, it is revealed that Arthur Petrelli took his sons Peter and Nathan on a hunting trip. Peter was too frightened to kill a deer so Nathan killed it for him.
Bart from The Simpsons is initially sent to a steel factory on account of Homer fearing he might become gay. It backfired, as the factory was full of Camp Gays, so Homer decides to go hunting with him.
In an early episode, Homer and Bart got lost in the woods. Homer set a trap to catch a rabbit. The trap threw it so far away Homer and Bart lost sight of it. Homer (at least initially) seemed to believe the rabbit would come back.
In Moral Orel, this trope is why Orel's father takes him hunting. Surprisingly, he does kill something, shooting a bear to protect his drunk father. He's so disillusioned by this point that he refuses to take credit for it when his father sobers up though.
A Looney Tunes short featured Sylvester and his son as house cats. When Junior told his Dad the other cats claim all that easy life spoiled what used to be the greatest mouser around. To show them wrong, Sylvester took his son to a place where he hoped to catch some mice. His failure cannot be solely blamed on the "giant mouse".
Gaston from Beauty and the Beast seems to think so and so does everyone in town. His sidekick sings that there's 'no one in town half as manly' while gesturing to a wall full of hunting trophies.
The Spectacular Spider-Man Kraven the Hunter, as Sergei Kravinoff he was a hunter who could take down wild animals with his bare hands, with nothing else left as a challenge to him he sets out to hunt down Spider-Man as the ultimate prey.
In The Legend of Korra, Tarrlok and his brother Noatak/Amon are forced on "hunting" trips by their father, who forces them to learn the art of bloodbending and practice it on animals.
There's a joke out there which says that "vegetarian" is an old Indian word for "bad hunter."