Truth in Television. Normally, adrenal glands and the brain's limiters make it so that you only use around 20% of your muscles and maintain a thought of self-preservation. Putting a loved one, child, or sufficiently close friend of somebody in danger is the fastest way to see the brain release said limits and let adrenaline kick in. All thoughts of self-preservation (and just about everything else that makes shy, meek people shy and meek) are overridden, and it is quite likely that several dozen of your bones will be broken (if you are lucky) before they let up. People who manage to enter Tranquil Fury instead of all-out anger are even more dangerous.
Wolves mate for life, and a male wolf will fight even to the death to protect his mate and offspring (in the last case, often in a tag team with Mama Wolf). He is also involved with raising the pups, taking charge of the youngsters, and teaching them how to hunt. (Hence, trope title.) Swans also mate for life - they might look serene and peaceful and cute, but just try to touch a cygnet when Papa Swan is nearby. I dare you. (...Did we mention that the wingbeats of a mute swan can break a human arm?) As an aside, all the mammal examples are the exception, as in contrast to most birds, most Real Life mammalian males, bears and monkeys in particular, are more likely to kill and eat their offspring than anything else (polar bear males even make it a lifestyle), usually causing their mates to go Mama Bear on them.
Don't dare mess with the boncies either, they'll swoop down and smash your skull with their beak. Without even stopping. Probably a good thing they ony live on isolated Scottish islands.
Male lions are protective of their own cubs. Other males' cubs, however, are fair game. (Though this is the case with almost every animal, and lionesses will also kill foreign cubs if given the chance, despite being very good mothers to their own.)
Male gorillas are normally very gentle creatures. Mess with their babies and you won't have very long to live.
In fact, several male non-human primate species that take on an equal or greater role in parental care are this, such as gibbons and tamarins.
Mockingbirds will attack anything that they consider as a threat to their chicks.
Same-sex couples do occur in swans and other monogamous birds, which sometimes get to raise kids. Now try getting anywhere near a cygnet with two Papa Swans.
In all ratites, large flightless birds like the ostrich, the male either has the sole task of incubating the eggs and raising the chicks, no input whatsoever from the mother, or he hatches and raises them in alongside the mother, which is done with the family after laying the eggs. So the male, now with a bunch of eggs and later chicks to raise alone, gets monstrously fierce. All ratites, from emus to rheas and even the small tinamous, attck anyone and anything daring to get close to the eggs/chicks, but the cassowary is the one that genuinely earns the price, for it has been able to horribly maim and even kill people just to protect its young.
To elaborate, one of the cassowary's toes on each foot is essentially a STILETTO.
There's a very good reason Papa Goats have big horns.
As do rams. Sheep may normally be the poster children for docile creatures, but unless you're their shepherd, don't enter a pasture after lambing season. Even walking past outside the enclosure will rate you a Death Glare.
True of piranhas, believe it or not. Piranha eggs are guarded by their father, who'll take bites out of anything that threatens them until they hatch.
Birds of prey. ANY. Just dare to approach an eagle's nest while the young are still there and see who's on the welcome committee.
Real life ganders aren't far removed from the one in Charlotte's Web mentioned above. The goslings are cute, fuzzy little things, but you must resist the urge to pet them if you don't want both the goose and the gander to tear you apart.
Speaking of Charlotte's Web, you'd never guess that some arachnids are this. Opiliones, a.k.a. the daddy longlegs, take on the sole duty of egg protection. They're LITERALLY a daddy longlegs!!
A conspiracy nut had been pestering Buzz Aldrin and other Apollo personnel, and he put up with that good-naturedly. But when said nut made an unfriendly move toward Aldrin's granddaughter, the 72-year-old astronautthrew one punch and knocked the guy out. (Well, seriously, even if there was any chance at all that the moon landing was a hoax, there was a reason Aldrin made Colonel in the United States Air Force, and that guy should have realized it.)
He was frequently noted to have treated his students like his own children, making his Heroic Sacrifice and Papa Wolf reactions all the more heartbreaking. Unarmed and faced with a cold-blooded killer, Librescu did the only thing he could to protect his students and used himself to barricade the door.
Tom Wanyandie, a 78 year old Cree Indian wilderness guide who fought off a literal Mama Bear attacking his son while screaming every profanity of his native language.
Bruce Lee was known for taking challenges from aspiring martial artists. During the making of Enter the Dragon, a Too Dumb to Live challenger snuck into their home and scared his two children, Brandon and Shannon. An enraged Lee put the idiot in the hospital with one kick.
Vance Flosenzier, who fought off a motherfucking shark when it was attacking his nephew. Not only did Flosenzier immobilize the shark and free his nephew, he then dragged it to shore so that park rangers could shoot it.
Sun Quan, leader of the southern kingdom Wu during China's three kingdoms period. When Cao Pi declared himself emperor of the powerful northern kingdom of Wei, Sun Quan agreed to act as his vassal. But when Cao Pi requested that he send his son Sun Deng to the north as a hostage (and therefore a guarantee of loyalty), Sun Quan cut off relations with Wei, declared himself emperor of Wu, and basically told Cao Pi to bring it on.
Quite sadly, Sun Quan eventually did outlive Sun Deng, who died of an illness. Based on some of his irrational and self-destructive decisions in the following years, it appears Sun Quan came noticeably unglued as a result.
One story about Genghis Khan claims he killed a man personally who made only a casual insult towards one of his daughters. (He said she looked like a frog, which in Mongolia at the time was the equivalent of telling a person he had loud clothes.)
Supposedly professional wrestler Kensuke Sasaki actually adopted Katsuhiko Nakajima, who debuted in the business in his teens, to act as this both in physical presence and through the Kensuke Office organization, which is essentially a "brand name" for their family (Kensuke Sasaki and his wife, female legend Akira Hokuto also have two biological sons) and affiliated wrestlers.
An Inversion of this is when Scipio Africanus the great hero of The Roman Republic saved the life of his father at the Battle of Ticinus. According to another version it was a loyal slave which leads one to cynically suspect that the slave got shafted when the tale was told. Of course it could have been Scipio and the slave working together and in fact it is not unlikely. But in any case this story was an example of "cub wolf" saving Papa Wolf. Of course this cub had pretty sharp teeth and came from a Badass Family.
Another possibility is that the slave was adopted as his son, not unheard of in Roman times.
Paparazzi don't bother Johnny Depp's family at home. Why? Because he's told them in no uncertain terms that if he catches any of them sneaking around his home taking pictures of his kids, he'll bite their nose off.
He once swung at a paparazzo with a piece of wood for trying to take pictures of partner Vanessa Paradis while she was pregnant with their daughter.
Jody Plauchet was abducted and raped by his karate instructor. Jody's father Gary planned for 10 days to kill his son's rapist and did so as he was being walked through an airport terminal. Despite a clear cut case of 1st degree murder Gary Plauchet only plead guilty to manslaughter and served 5 years probation.
There are some quite gruesome stories about what the Russian government does when a Russian diplomat is kidnapped. Things like mailing them a photo of each of the hostage takers-inside a crosshairs. Or reciprocally kidnapping an associate of the original kidnappers and then sending a package to the hostage takers containing-a finger. The Russian government is not the most benevolent of governments, but when it comes to situations like this You do not want to mess with Mother Russia.
May 31, 2011, a bank robbery took place in Sarasota, Florida. As soon as the incident began, US Staff Sgt. Eddie Peoples placed himself between the robber and his young sons, then advised them to hide under some chairs and moved other chairs to cover them. Eventually the robber pointed his gun at one of the sons and said that if anyone tried anything, he'd shoot the kid. After the man left, Peoples followed him and used his own van to block the escape vehicle, then disabled the robber with hand-to-hand combat. In an interview with news sources, Peoples said "You don't threaten people's children."
This Ohio man who, after hearing his three year old son's screams upon falling into a well more than 40 feet deep, scaled the well's walls down to the bottom to ensure that nothing bad would happen to his little boy before the fire department arrived.
A man from Turkey saw his four-year-old son fall from a fifth story balcony and immediately jumped after him. Pushing against the balcony to gain momentum, the man grabbed his son mid-fall, wrapped his arms around him and then turned his own body over so that he would hit the ground instead of his son. The child was left completely unharmed while the father suffered from a broken shoulder and ribs.
Stuart Chaifetz is worried because his autistic child behaves oddly in school. He puts a recorder in the kids's clothes and finds out he's horribly bullied and abused by the staff. He's now on a crusade to protect all kids in such a terrible situation.
This instance of a father beating the alleged molester of his daughter to death.
A Chicago father held off the would-be kidnapper of his two-year-old daughter. Here.
Israeli politician and current Minister of Foreign Affairs Avigdor Lieberman once clobbered a kid who was bullying his son, and threatened to do it again if he did it again. He wound up apologising and paying compensation.
The "Push my kids and I will stab you" guy from Black Friday 2012 certainly fits among the darker examples of this trope.