Lone Wolf and Cub (one of the Western names for this was Shogun Assassin) had the main character (Ogami Ichirou) killing hundreds of the Shogun's troops, very violently. Said Shogun declares that he's willing to leave Ogami alone, but just to be a snit, his dear infant son Daigoro must die. ...so Ogami, as the good Papa Wolf that he is, destroys the rest, resulting in the viewer concluding that Shogun was an idiot for not predicting that.
In episode 7 of One Piece, when Buggy learns how much Luffy values the straw hat he got from Shanks, he tries to destroy it... which only provokes Luffy further. (To be fair, Buggy hates Shanks even more than he hates Luffy)
Bleach is pretty fond of these, the lead being The Messiah he can't actively seek combat so they use this as a method to make him. For example:
In the Shinigami Arc, the hollow that killed his mother (for worse, he was a little child back then, and she died protecting him).
In the Soul Society Arc, he was allowed to fight because they were going to execute his friend Rukia.
During the Arrancar's attack on the real world, they attacked his friends and family. And then, his dad got to off the hollow (now an Arrancar) that killed his wife and the lead's mom.
In the Hueco Mundo Arc, they forced his other friend Orihime to go with them via Sadistic Choice — it's even pointed out for that final closure (just in case taking poor Orihime away wasn't enough) that the Big Bad wants to destroy his home town so that he has fuel for his MacGuffin.
Due to their nearly symbiotic relationship, the weapons and technicians in Soul Eater frequently have each other as their Berserk Button, especially the female characters for the male ones.
In Mai-HiME, at least Mai is provoked this way when the first Monster of the Week targets her ill and weak-willed brother Takumi. Later events, in a subversion of this trope, imply that this is the standard method of "initiation" for most HiMEs, with the monster attacks carefully planned by the Powers That Be specifically to attack their loved ones to draw them into fighting.
In Weiss Kreuz, to get back at Ran "Aya" Fujimiya for his part in killing their boss, the Schreient girls kidnap his comatose little sister Aya-chan and hold her hostage, intending to kill her in front of him. This results directly in Aya rejoining Weiss to hunt them down and kill them.
Claymore: Threaten to rape/disfigure/brutalize the mightiest of an order of demonslayers pledged not to take human life? She says "Fine, I don't care," and thinks uncharitable thoughts. Kick around the girl that was following her around? She draws the guy's own sword and makes perfectly clear that, if the order in question has to put her down, he will still be dead. The failure of the bandit in question to keep that hint in mind when he finds said girl in a village the Claymore he threatened just left kicks off a Roaring Rampage of Revenge that was both brief... and total.
The Team Rocket trio's obsession with Ash's Pikachu in Pokémon is a classic example of this trope.
Lampshaded in thisVG Cats strip. Really, aside from a bad attitude about Poke Balls, Pikachu wasn't much different from any other Pokemon.
In Saint Seiya, Dragon Shiryu was almost dead by the hand of Cancer Deathmask, a purely evil Golden Saint who was completely immoral about murder, even killing children for the lulz. Cue to the image of Shiryu's stepsister Shunrei praying far, far away in the Rozan cascade. Cue back to Deathmask being upset about that and using his Psychic Powers to grab the poor girl and throw her down a waterfall in hopes of killing her and projects the image in Shiryu's mind to taunt him with what he just did. See the always calm, cool and collected Shiryu go absolutely batshit on Deathmask in his only ever Unstoppable Rage episode in the series, as Cancer's attempt at murder backfires on him big time.
In the Ea Cycle Morjin threatens to kill Valashu's family. He later follows on his promise. Brutally.
In Chrono Crusade, Rosette and Chrono probably would have never gotten into the demon-hunting business at all, much less try to stop Aion's plans, if it hadn't been for him kidnapping Rosette's brother in the first place. (That being said, he did have a good reason to go after Joshua.)
Literal non-example, in Black Lagoon Balalaika reminds the leaders of the other criminal organisations that her organisation will destroy anyone gets in their way,. And their families. And their pet dog, if necessary.
In the Read or Die TV series, both groups of The Men in Black choose to repeatedly target a normal writer for their sinister plan, despite it being easy enough to just find someone else. This leads her friends, various heroines who used to work for the groups, to rebel against them.
In Watchmen, while Rorschach is being taken back to his cell one of the prisoners threatening him promises to kill his mother, kids, sister, and...dog.
Similarly, Rorschach kills the dogs of a child-killer before killing the killer himself. Granted, the killer had fed the bodies of his victims to the dogs, but they're just dogs.
Squirrel Girl is convinced that she and the other Great Lakes Avengers shouldn't try to fight a villain who is on the verge of destroying the entire universe, and that they should leave it up to more powerful heroes. Until it is pointed out that if the universe goes, all the squirrels go with it. No! Not the squirrels!
The Wizard of Oz is the Trope Namer. The Wicked Witch of the West declares, "I'll get you, my pretty, and your little dog too!" just to show how evil she is by threatening Dorothy's beloved pet. It's actions like this that prove the Witch is evil, to justify Dorothy's eventual melting of the Witch.
In No Country for Old Men, Llewellyn calmly advises Chigurh not to threaten his wife. And then Chigurh kills them both.
It's even worse than that, Chigurh has already found the money he was looking for, and Llewellyn is already dead. Chigurh has absolutely no reason to kill the wife, other than to make good on his threat.
Cyrus "the Virus" Grissom of Con Air just might have lived and escaped if he didn't make the terminally stupid mistake of telling Cameron Poe (the hero) "Before I kill you, I'll let you know that the last thing that little Casey Poe (your daughter) will ever smell will be my stinking breath." Sure enough, cue Heroic Resolve from Cameron, and a hilarious Karmic Death under a rock-crusher (don't ask) no more than five minutes later.
Subverted in The Usual Suspects. Drug dealers rape Keyser Soze's wife, cut his son's throat in front of his eyes, then threaten to kill the rest of his family unless he hands over his turf. He responds by killing the two of the drug dealers, then the rest of his family, then hunting down the drug dealers' families and everyone they've ever known or done business with, while the narrator explains that Soze's real strength is his willingness to do what the other guy wouldn't.
Aliens: Do not kidnap Newt and turn her into a cocoon. Unless you want to get your nest torched and Thrown Out The Airlock. "Get away from her, you bitch!" indeed.
Biff A has done this to Lorraine in Back To The Future Part II. When Lorraine A threatens to walk out, Biff A threatens to also cut off her children - leaving Lorraine A with no choice but to stay.
If the Green Goblin of the first Spider-Man movie really fancied himself a "villain" like he so proudly did, he surely would have knew that telling Peter that "M.J. (your girlfriend) and I... we're gonna have a hell of a time!" while waving a phallic weapon in his face would give Peter the righteous rage to kick his armored-ass to hell and back; and Peter did.
To top it off, in the sequel, the one thing that has Peter spring back into action and regain his powers is Dr. Octopus kidnapping Mary Jane.
In The Patriot, it is Col. Tavington's pathological targeting of Benjamin Martin's family that turns the protagonist from a mild-mannered pacifist to a furious hatchet-wielding 'ghost' who wins the Revolutionary War single-handed empowers militia forces and inspires his compatriots to victory.
Lampshaded in The Western movie Silverado (1985) when corrupt town sheriff Cobb indicates to Paden that he'll harm the dwarf female bartender if Paden moves against him, even though Cobb acknowledges she has nothing whatsoever to do with their dispute. He does however know Paden (whom he used to work with when they were robbers) got caught while protecting a wounded dog he'd previously claimed to despise, so figures the threat will make Paden back off. It works at first, but the bartender figures out what's happened and talks Paden into fighting Cobb anyway.
In Jumper, the villainous Paladins claim that they hunt Jumpers because only God should have that power and mortals will abuse it. Considering David's behaviour, they might have a point. Then they kill his father for little good reason.
In Iron Man 1, the Big Bad paralyzes Tony Stark and steals the minature arc reactor implanted in his chest that keeps him alive. As he leaves, he tells Tony, "It's a shame you had to involve Pepper (Tony's assistant) in this, I'd have preferred that she lived."
Moriarty in Sherlock Holmes A Game Of Shadows makes a point of attacking and threatening Watson just because he knows Holmes holds him in high regard. Holmes even goes to Moriarty's office on Watson's wedding day to plead with the professor not to involve him in their ongoing conflict, only to be told that Watson is 'collateral damage' and the professor has already made sure to send his 'regards' to the happy couple (in the form of a squad of assassins who attack Watson and his bride during the train journey to their honeymoon).
The corrupt agent Atwood in Timecop won't testify against the Big Bad he's secretly working for because "He'll send somebody back to wipe out my grandparents. It'll be like I never existed. My mother, my father, my wife, my kids, my fucking cat!"
A literary example: In The Aeneid, Aeneas' rival and counterpart Turnus kills Aeneas' good friend, the innocent youth Pallas; at the end of the epic, Aeneas is about to spare Turnus' life when the sight of a baldric stolen from Pallas reminds him of the murder and drives him into a killing rage.
Skinwalker: I will come for you. I will kill you. I will kill your blood, your friends, your beasts. I will kill the flowers in your home and the trees in your tiny fields. I will visit such death upon whatever is yours that your very name will be remembered only in curses and tales of terror.
A particularly cruel example in Holes, where after the town had found out about Miss Katherine and Sam's relationship, they also killed Sam's beloved donkey Mary Lou, right after killing Sam himself.
In the Dale Brown novel Wings of Fire the Libyans kill Paul McLanahan and abet Pavel Kazakov's henchwoman killing Wendy McLanahan.
In Air Battle Force, General Gryzlov threatens Patrick McLanahan's friends, bases, crews, aircraft and son. He tries to make good on this in Plan of Attack, but doesn't completely succeed.
In the Honor Harrington books, Cordelia Ransom, head of Public Information, planned to kill Nimitz, Honor's treecat companion, purely to break her before the cameras and to enrage her fellow captives so that they would attack and could be stripped of the protections of prisoners of war.
Played with in the novel White Plume Mountain. One of the villains actually says "I'll get you, and your little dog too!", but the dog in question is neither innocent nor helpless. The "dog" is a sentient, fire-breathing hell-hound skin.
Live Action TV
In Smallville, even Jor-El does this on occasion due to his Adaptational Villainy. Like in Arrival when he freezes Chloe almost to death. There is also the time in Splinter when he infected Martha with a deadly virus which turns out to be a trick by Brainiac, but Clark totally buys it.
The original series of The Black Adder has the villainous Witchsmeller Pursuivant burning an innocent old woman as a witch, and her cat on a correspondingly smaller stake. He later sneers in the face of the cat-loving Percy that he burnt "Mistress Scott...and her pussycat!" He gets a spectacular comeuppance, after which Percy wisely comments, "I SAID he shouldn't have burnt that cat..."
Rita Repulsa in Power Rangers refused to attack any city other than Angel Grove, despite it being the one city that was protected by a force capable of challenging her.
At one point in Hercules: The Legendary Journeys, Herc goes into the underworld to visit his family, who were murdered by Hera. With his family is their dog, and on the commentary, Kevin Sorbo notes something like, "You can tell she's evil, she even killed my dog!"
In the second season premiere of The Sarah Connor Chronicles, a rather enraged Sarkissian attempts to get revenge on the Connors by assaulting their house, car bombing Cameron, and beating the Connors senseless. Sarah and John are unable to resist....until Sarkissian tries to rape Sarah. John very quickly drops all pretenses of Thou Shalt Not Kill, and delivers a highly righteous (if offscreen) ass-kicking.
This is later shown on a flashback.
On Angel, Daniel Holtz starts out by getting revenge on Angelus - by harassing the souled Angel. Initially, Angel responds with sympathy and guilt with what his soulless self did to the troubled man - and tries to simply reason with him. When Holtz starts to threaten Angel's (innocent) friends, that's when Angel realizes that more drastic action needs to be taken.
Glee Subverts this in this threat from Sue Sylvester:
I will go to the animal shelter and get you a kitty cat. I will let you fall in love with that kitty cat, and then, on some dark, cold night, I will steal away into your home and punch you in the face.
A recurring tactic of immortals in the Highlander TV series, although there is a practical purpose to it. By destroying the loved ones of their immortal rivals they hope to cripple their will to live, making them an easier fight (Who Wants to Live Forever, after all?). Naturally, this can, and has, backfired.
Person of Interest: One of the assassins after the Fixer, they stated to kill her and her driver too.
Scandal: Becky, Huck's girlfriend, murders the entire family he keeps an eye on. Oh, and she literally killed their dog too.
One of Breaking Benjamin's songs, "Home", makes a lot of The Wizard of Oz references, including this line, "cause I’m gonna get you and your little dog too".
Quite literal in the board game expansion of Kill Doctor Lucky. Aptly named Kill Doctor Lucky and His Little Dog Too.
The Dungeon Master's Guide lampshades this as a tactic for a DM to develop a campaign setting called "Hitting the PCs Where It Hurts"—having the son of a blacksmith they befriend become kidnapped by slavers, for example, or having a peaceful village they love to visit be in the path of an evil cleric's invading army. It also warns not to overdo the tactic, however, or otherwise the PCs will never grow attached to anything for fear of putting it in danger.
Compared to the Transformers, humans are tiny, weak, and fragile, but possess heart and guts far beyond their size... which makes the Autobots extremely protective of them. Naturally, the Decepticons just have to pick on the humans instead of quietly sneaking off and conquering a planet the Autobots haven't adopted yet.
If players in Fable II didn't have sufficient motivation to stop Lucian before, they will once he murders the player's spouse, children and dog.
Keep in mind this is after he kills your sister.
In Fallout 3 Enclave Dragon Autumn shoots a research assistant in the head to 'motivate' the main characters father. This despite the fact that he had total control over the situation, and she couldn't possibly have been a threat.
The Big Bad of The Darkness video game (if you don't count the Darkness itself) is a mob boss named Paulie "Kill The Children Too" Franchetti.
Parodied in Tales of Monkey Island Chapter 1, when the Marquis De Singe is defeated by Guybrush and leaves, promising to have revenge on him and his little hand too.
In BioShock Fontaine threatens to kill all the rescued Little Sisters: "When you're cold and stiff, I'm going over to Mother Goose's house, and I'm going to take it apart, piece-by-piece and brat-by-brat. Consider it your legacy."
Used in, of all things, Professor Layton and the Unwound Future, where the Big Badkidnaps Layton's adopted daughter in order to make absolutely sure that Layton will pursue him. The irony is that Layton, being Layton, would have gone after him anyway — all this trick did was make himmad.
In Jade Empire's backstory, the Emperor punished his traitorous brother Sun Li by ordering the Lotus Assassins to kill his family. The assassin ordered to do so rebelled halfway through and spared Sun Li's daughter.
In the Champion mission of Assassins Creed Revelations, you initially have to defend a printer from the eponymous Templar. In the second part, the Champion goes after the printer's father instead.
The Final Boss of Dragon Age II can sometimes grab one of your party members, with a different dialogue snippet for each of them. If they go after Hawke'sLove Interest, the speech is aimed at Hawke rather than the victim.
"How does it feel, Champion, to know I hold the life of the one you love in my hands?"
Axe Cop advises people how to defy this when they become crime fighters (which he recommends as the ideal career) — "Your family should hide in the bushes outside your house with guns every night. Because bad guys are always trying to kidnap your family if you are a crime fighter."
This one of several things that consistently provokes the Avatar State in the normally sweet and pacifist Aang in Avatar The Last Airbender. In the first of season two, some unnamed Earth Kingdom general tries to provoke Avatar State by sinking Katara in rock, which turns out to be a bad idea. Appa is also a frequent target.
Likewise, Katara will not stand aside while Aang gets hurt. Azula and later Hama learned this the hard way.
In the Ben 10 episode Ken 10, Kevin Levin stomps Ken's rock dog-thing, just to provoke the kid into attacking him. It gets better by the end of the episode, naturally.
In an episode of Cartoon Planet, Zorak is forced by Space Ghost to give Brak lessons on being evil. He does this by telling him to threaten Space Ghost "and your little dog, too". Brak objects to the notion of harming Space Ghost's (non-existent) dog and asks him to blast Zorak, to which Space Ghost happily complies.
In one episode of Batman Beyond, Terry is fighting a mutated Dr. Cuvier, and Ace, Bruce's pet Great Dane, is also present. Now, the two have had a turbulent relationship so far, but when Terry gets hit, Ace rushes in to fight off the monster, only for the monster to wrap its tentacles around Ace and tries to do him in. And that's when Terry got pissed.
In the final episode of Superman The Animated Series, Superman gives Darkseid an And This Is for... punch for Dan Turpin, whom Darkseid murdered at the end of his foiled invasion of Earth. Darkseid responds by claiming that "Had I known one human's death would pain you so, I would have killed more." When Darkseid gets the upper hand in their fight right after this, he adds "And kill more I shall! Carry that with you to oblivion, Superman!"'
Used in Young Justice when Desaad threatens Superboy and his dog... er, wolf:
Desaad: "Kill the boy, and his little dog, too."
Hoodwinked: The Wolf says "You can't hold on to those recipes forever! I'll get you and your little Granny, too!" after Red tricks him into falling into a river.
Adventures of the Gummi Bears: In the episode "Eye of the Beholder", when the witch who has enchanted herself too look beautiful and put the whole of Dunwyn Castle (including the king) under her spell is finally exposed, she threatens to get princess Calla, "and [her] little pig too" (Sunny is disguised as a pig to avoid being spotted by humans).