Although not a biological father, O'Malley from The Aristocats fights quite ferociously to prevent the Big Bad from shipping the cats to Timbuktu.
Dr. Tenma in the 2009 Astro Boy film. After he accepts Astro for who he is, it's made clear that he's willing to face the military, its angry Commander in Chief, and its scary indestructible robot to protect his boy. Makes you wonder what would happen if you threatened Astro while there was a chance Dad might get his hands on you.
Gru from Despicable Me after his 3 adopted daughters are kidnapped. Among other things, he hopscotches over a group of heat-seeking missiles fired towards him and one-punches a shark!
In a minor case, when the carnival barker denies Agnes the unicorn she wanted, even when she hit the nearly impossible target. He almost made her cry and Gru shows him why he should never mess with the adopted children of a supervillain.
Marlin in Finding Nemo, because how many fish do you know would risk life and death across an ocean that is infamous for some of the most POISONOUS and DANGEROUSLY VICIOUS creatures of the sea, to find his son? He's not even a shark, he's a goddamn clownfish who's scared of everything.
In How to Train Your Dragon, Hiccup's father is a Badass Viking who's willing to punch dragons in the face and dent metal with his hammer to protect his boy, and the other is a freaking dragon. A dragon who attacks and drives off another dragon a little over three times his own size when the other threatened Hiccup.
The Lion King: Mufasa is the best father ever (no matter his species), as he is wise, just, loving, stern when necessary, and royal. But don't you dare cause any harm to his kid, or he will find you and he will kick your ass (unless you're unlucky...).
Invoked in Away We Go when the expecting parents are discussing their future daughter.
Verona: [Do you promise] that her fights will be your fights?
Burt: I do.
In Back To The Future Part II, Marty gets chased out of the "dark 1985" version of his house by a baseball bat-wielding Papa Wolf, who is enraged to find Marty in what, in the altered timeline, is the bedroom of the Papa Wolf's young daughters. Based on what he's screaming, it's not the first time people had broken into his home.
OTOH, he also plays more than one real Papa Wolf out there.
John Wayne spends the majority of Big Jake tracking down and in the end blasting seven hells out of a bunch of bandits who kidnapped his grandson. Grandpa Wolf, indeed.
Universal's 1934 movie The Black Cat gives us Dr. Vitus Werdegast (as played by Bela Lugosi), who takes revenge on Poelzig for killing his daughter (among other things, but that was what sent him over the edge). by skinning the man alive on his own embalming rack. And what's worse is that only a few moments earlier, he had been given hope that his daughter was actually alive after thinking that she had been dead since he's been sent to the prison camp.
The Blind Side: Coach Cotton has a Papa Wolf moment after the Opposing Sports Team deliberately kicks Michael when he's down and after the play has already ended, and the referee not only ignores the kick, but penalizes the Wingate Crusaders.
Coming to America provides a nonviolent example in Cleo McDowell, an amiable and slightly Bumbling Dad who's eager to marry his daughter Lisa off to a rich boy. He's therefore over the moon when he discovers her suitor Akeem is actually a prince. But when Akeem's father King Jaffe upsets Lisa, McDowell drops the bumbling act and angrily threatens to "break a foot off in your royal ass."
Colonel Badass Ahnuld from Commando acts pretty unassumingly in civil life, but when the villains kidnap his pre-teen daughter...
Whenever Arnold Schwarzenegger plays a father in any of his action flicks, expect some seriousPapa Wolf action to go down if the bad guys mess with his kids. Case in point: True Lies — when the Big Bad kidnaps Harry Tasker's daughter, Harry goes after him with a fucking Harrier jet fighter. And sends the Big Bad on a missile ride.
Arnie plays a mild-mannered ex-military helicopter pilot (who takes skiers up mountains) in The 6th Day. He fails to die on schedule, and the company responsible kidnaps his wife and daughter to try to force his compliance. Then he and his clone (yes, it's that kind of movie, and why he was supposed to be dead) destroy the company with a tin of aluminum oxideand one pistol between them. If you can't say Made Of Awesome, I'll do it for you.
Death Sentence: Nick Hume's older son gets killed by a gang member and he learns that the gang member will only receive a few years in jail, he forces the case to be dropped so that he can kill the bad guy himself. In doing so, he is forced to kill another member of that gang. However, the gang's head doesn't take kindly to this and swears vengeance on Nick's family. Nick being an Action Survivor rather than a hardened Badass, he fails to stop the gang. Though his younger son survives and he gets back at the gang successfully, it's quite clearly shown that Nick ends up far from the man he used to be. Not all positively.
An unusual although understandable example would be Walt from Gran Torino, who is Papa Wolf toward his neighbors once he gets over some racial tension, but not toward his "own spoiled-rotten family" who treat him more like an invalid than a worthwhile individual. When he comes to Sue's rescue:
Walt Kowalski: Ever notice how you come across somebody once in a while you shouldn't have fucked with? (spits on the ground) That's me.
James Potter in Harry Potter. He decided to take on Voldemort on this own, knowing it almost certainly meant death (he even said to Lily "I'll hold him off", indicating he knew he stood no chance) because it gave his wife and son a chance of escaping.(He wouldn't have had a chance against the Dark Lord anyway, but on top of that, he wasn't holding a wand. It makes this into a Heroic Sacrifice.)
An Action Dad score for Denzel Washington is John Q., where to make sure that his Ill Boy son Michael will get a heart transplant which is being denied to him because insurance doesn't cover it, John Quincy Archibald actually takes a full hospital hostage and claims he won't back off until Michael is given priority. John goes as far as improvising a Thanatos Gambit so his heart will be harvested and given to his child, but it fails. In the Bittersweet Ending, however, John is still trialed and incarcerated, but Michael is saved.
His Spiritual Successor, Sonny Koufax in Big Daddy, is no slouch himself. He at first takes a boy as his own son to raise out of undisguised selfishness, but thanks to Becoming the Mask, ends up declaring: "I would die for this kid, just so he wouldn't have to feel a moment of sadness."
Parodied in Last Action Hero, where the movie from which Arnold's cop character is lifted includes a face-off with the Big Bad who abducted his kid.
The premise of The Last House on the Left is about a group of people who get trapped inside a house with a Papa Wolf and a Mama Bear after they brutalize and rape the couple's daughter. Three guesses as to what happens next.
Later went on a rampage across San Diego just to find his baby. It doesn't help that he was high on amphetamines.
In the classic film Ma and Pa Kettle,Ma,Pa, and their large family move into an ultra-modern house Pa had won in a sweepstakes. Eventually Pa gets fed up with all the newfangled gadgets in the house, and moves back into the family's old home: a decrepit shack in the middle of a swampy junkyard. Meanwhile, Ma holds the police at a standoff with a shotgun after she learns the contest was a cruel publicity hoax. It takes the intervention of the Kettles' adult eldest son to bring her out of her rampage. Just as the woman who orchestrated the hoax decides not to press charges and offers Ma her most sincere apology, here comes Pa Kettle with the family wagon and a dozen or so of his Injun friends.
Tommy Lee Jones also played a Grandpa Wolf in The Missing. He was a Disappeared Dad and Grandpa hoping to try getting his family's forgiveness... and arrived back home just in time to learn that his eldest granddaughter has been kidnapped and was about to be sold as a child bride. So when his daughter (played by Cate Blanchett) went Mama Bear to get her girl back, he decided he wouldn't be less and joined her cause. So much that he defeated the Big Bad via Taking You with Me, killing himselfin the process.
The role that followed that one was Man in the House, where he's a sheriff who has to protect a bunch of cheerleader girls after they witness a murder. Hilarity Ensues until not only one of the girls is almost killed by a car bomb, but the man's daughter is kidnapped...
Liam Neeson's character in Nell, who winds up very protective of the borderline Wild Child (wild adult, by then) he and another doctor have been observing since her mother's death. A reporter who sneaks up trying to get a picture of the rumored "wild woman" gets thrown down the front steps of Nell's cabin and his camera broken for his troubles. Neeson's character does admit he overreacted, only to chase the reporter away when the idiot keeps asking questions.
In North Country, Josey's dad. He was initially aloof about his daughter for reasons relating to her first pregnancy (where she was apparently promiscuous), although he eventually stood up for her at the union rally when she tried to expose the sexual harrassment problems at the mine she works at, also calling out his coworkers on this fact. However, the biggest example of his being a Papa Wolf comes in later: During the trial, Josey is forced to reveal what truly happened during her youth and the real reason she became pregnant with her son after one of the co-workers (who she also went to school with) exposed the knowledge of who the father of her first child was: It turns out that her teacher had in fact committed statutory rape on her after serving Saturday detention for skipping class and kissing said future co-worker, of which the only witness was said co-worker and he failed to stop him. As soon as the father learned the truth during the trial, he walks over to the teacher and then proceeds to go ballistic and attack him for raping Josey, resulting in him being forcibly removed from the courtroom.
The movie Orca: The Killer Whale has the titular killer whale, seeking bloody vengeance against the man who killed his mate and calf.
What's now known of orca social behavior makes this unlikely to be a literal example of this trope. A son retaliating for the death of its mother, now...
Stacker Pentecost and Hercules Hansen in Pacific Rim. Both have piloted Jaegers since their inception and destroying Kaiju is their number-one priority in life. Pentecost is also Marshal of the Pan-Pacific Defense Corps and former pilot of Coyote Tango; Hansen is the oldest Jaeger pilot still on active duty and drifts with his son, Chuck, in Striker Eureka.
Benjamin Martin in The Patriot is firmly against a war for independence and submissive towards the over-the-top villain...until his farm is burned down, one of his sons is killed, and another is arrested and taken away to be hanged. Then he goes after the Redcoats with muskets and hatchets...
The Professional: Léon becomes a surrogate father to the orphaned Mathilda and protects her on her quest for vengeance, taking on the entire NYPD in the process.
Coach Jones of Radio becomes this on several occasions for Radio. In one instance, he slammed the Jerk Jock that tricked Radio to enter the girls' locker room into the trophy case display, after the eye-opening words of, "Son, it's times like these I wish I wasn't a teacher so I could do what I really want to do to you."
There's an excellent case for Mr White fulfilling this trope in Reservoir Dogs in his protectiveness over young protégé Mr Orange, to the point where he takes a bullet for him. He really, really doesn't like it when you accuse Orange of being a rat. When Orange indeed turns out to be the rat, Mr. White has to put the bullet to him in probably the most emotional moment of the entire movie.
The butler Cadbury in Richie Rich is something of a second father to Richie. The scene where Ferguson mandhandles Richie in the beginning of the movie says it all.
Ferguson: It's my job to protect him.
Cadbury: I know Mr. Ferguson, but touch him that way again and it is YOU who will need protecting.
In Romeo Must Die, Isaak finds out that Mac was the one who murdered his son and proceeds to strangle said person without any hesitation.
Charlie Anderson in Shenandoah insists that the Civil War doesn't concern his family, even saying that his sons don't owe their state anything because the state "never came around here with a spare tit." But when some Union soldiers mistake his youngest for a rebel and take him prisoner, he starts taking the war personally.
As opposed to the king in the original fairy tale, in Snow White: A Tale of Terror Frederich goes out into the storm on his horse to find Lilli when he hears she's missing.
Pops from Speed Racer puts his Greco-Roman wrestling skills to work while protecting his family from ninjas, er, non-jas.
Liam Neeson's Ex-Special-Forces commander Bryan of the film Taken (see page quote) shows the organization that kidnapped his daughter the exact reason why you don't screw around with an ex-CIA operative's kids. In a particularly brutal example of this trope, he is willing to go as far as threaten to kill a Corrupt Cop and former friend's innocent wife AFTER winging her with a bullet to show he's serious to save his daughter from being sold into prostitution. The entire movie is effectively a paean to the Papa Wolf trope.
Subverted by Keyser Soze in The Usual Suspects. In a tale told in universe, some Turkish mobsters break into Soze's home and brutalize his family, holding them hostage. When Soze returns home, he promptly pulls a gun on the mobsters... then turns the gun on his family, saying he'd rather they die than live another day.
Sir John Talbot in The Wolfman (2010). He shoots on those who want to catch his son, and later tries to kill Lawrence. And he already killed Ben. And he is a werewolf.