The whle plot of The Hunger Games is structured around the idea that the capital is more than willing (and happy to) kill children in order to keep the districts in line. "Psh, we'll just kill their children! That'll prevent another uprising!"
Queen Cersei has as many of her husband's bastard children murdered as possible, including an infant still at her mother's breast. Also, when Tyrion Lannister asks the sellsword Bronn if he would go as far as murder an infant without asking questions, Bronn replies, "Not without asking questions. I'd ask, how much?". Ouch.
Cersei's daughter Myrcella gets horribly disfigured by Darkstar, her ear cut off and her cheek slashed to the bone.
There are the slave children crucified to show Daenerys the way to Mereen.
Robert's attempted assassination of the 14-year-old, pregnant Daenerys almost certainly falls under this.
Arya loses two friends to this trope: Mycah is killed by the Hound, while Lommy made the mistake of believing that Gregor Clegane's men Wouldn't Hurt a Child.
Even the good guys aren't immune to this: implicit in the fact that Ned Stark took Theon Greyjoy hostage was the assumption that if Lord Greyjoy tried to rebel again, Ned would kill Theon.
And in return, Theon kills Bran and Rickon Stark as soon as he takes over Winterfell. Except he doesn't, and technically kills two lowborn kids who look like them (implied to be his own bastards, no less.) But the trope still stands.
This trope is the establishing moment for both Jaime Lannister and the series as a whole. "The things I do for love" indeed.
Jaime also threatens this to Edmure Tully, and provides the page quote. Whether he would have followed through in that instance remains an open question.
In the backstory, Gregor Clegane slammed a baby's head against a wall then raped and murdered the baby's mother while she was still stained by her dead son's blood and brains. His companion Amory Lorch killed the woman's three year old daughter. He was pretty sadistic about it too: the frightened little toddler kicked him, and he stabbed her fifty times with a sword in a fit of rage.
Author Andrew Boland, just loves this trope. In his novel Hell's Children, a little boy’s head explodes. Did I mention that a little girl is tortured, then raped, and then has her arms, legs, and eyes, amputated. Oh and, at some point in the story, a man cuts out the brain of his own son.
Voldemort's first known act in Harry Potter is to attempt to kill a baby, and his Death Eaters attack muggle children just as much as they would muggle adults (including one scene in the 7th book where Voldemort kills a family). If teenagers count, his Death Eater followers aren't above torturing Hogwarts students in the 7th book (and ordering students to torture each other), and Umbridge makes rule breakers write lines using their own blood with a magic scarring quill and seriously considers using the (most illegal) torture curse on the students.
In the seventh book, one of the Carrows decides to pin a screw-up on some Ravenclaw students and hand them over when Voldemort shows up. Said Ravenclaws are first years. First years are eleven years old.
In The Silmarillion, the sons of Fëanor commits all sorts of nasty things, but even they do not willingly hurt children; the murder of the sons of Dior is left to one of their "cruel servants" (although they were arguably responsible for the occasion arising).
Stephen King. Usually in horror, kids are safe. Not in Stephen King's universe. He'll kill a kid. This is especially apparent in IT, where the very first person in the novel to bite it is six-year-old George Denbrough, the little brother of the main character.
Just to make this painfully apparent, the way he dies: he's half-drowned in a drain and then has his arm ripped off at the joint by a Monster Clown.
Rare Female Example occurs with Lady Macbeth. The violence is only implied, but at this point in the play, she seems perfectly capable of going through with it.
Lady Macbeth: I have given suck, and know
How tender 'tis to love the babe that milks me:
I would, while it was smiling in my face,
Have pluck'd my nipple from his boneless gums,
And dash'd the brains out, had I so sworn as you
Have done to this.
Not just implied with Macbeth, who has assassins murder Macduff's wife and young son. His wife is horrified by this, though not because of the children — it screws up her political machinations. That said, those particular murders do feature among the things she mentions in the infamoussleepwalking scene.
The Thane of Fife had a wife; where is she now? What, will these hands ne'er be clean?
Older Than Radio: In the original Frankenstein, the Monster kills his creator's much younger brother William in a fit of rage, and then frames the child's nanny for the murder.
In Alex RiderJulia Rothman and other members of Scorpia have the majority of London school children injected with nano-capsules containing cyanide, and plan to dissolve the capsules if the UK government does not accede to an impossible request. Rothman herself also has Alex injected- after not being able to watch his father's death in person, she wants to see the son's.
In the first book, the mastermind's plan is to have a deadly disease released into every school in Britain.
Actually, given their treatment of Alex, this trope could apply to almost any villain in the series- and arguably even to MI-5. They wouldn't hurt Alex directly, sure, but...
Pick a Graham Masterton novel, any Graham Masterton novel (but especially Night Wars). Then, ask whether or not the villain believes in Infant Immortality. The answer is "no."
Killer, in Marti Steussy's Forest of the Night. Big Eyes gets underfoot; Killer swats him like a fly.
Several in The Pale King. At least one adult directly attempts to kill Leonard Stecyk as a child. Another hits him with their car, though it's debatable if that was accidental. The rest of them have a little more restraint. There's also an unnamed man in Chapter 8 who is implied to be a sexual predator. And the man who murders Toni's mother in front of her.
In Death: A number of criminals in the series would happily do this, and so much more. Eve and Roarke's parents engaged in this trope.
In the Warrior Cats series, there are a couple examples. Brokenstar insists on brutally training kits at too young an age, and actually fights them himself in training, killing them. Tigerstar kills Gorsepaw in The Darkest Hour for no other reason than to bring fear to WindClan. Darkstripe also attempts to kill Sorrelkit because she caught him meeting Blackfoot on their territory.
Many of the villains of the Redwall series are like this, the most notable being Slagar the Cruel, who kidnaps children and sells them into slavery, not hesitating to abuse and torment them along the way, often just For the Evulz. There's the guy that he's selling them to, Malkariss, who keeps hundreds of children as slaves in his underground kingdom, ruthlessly abusing and overworking them for the rest of their lives. Vilaya the Sable Quean also does a similar thing when she is Genre Savvy enough to kidnap the Redwallers' children as ransom for the Abbey. She takes it a step further when she mercilessly kills one of them with her poisoned knife and threatens to do the same to the rest of them if they don't behave. Then there's Razzid Wearet, who makes it a point that he enjoys eating children. Cluny the Scourge also makes a passing thought about eating some young rabbits that he sees. And minor villain Warpclaw threatens to and almost kills a baby shrew. Mokkan also gives a viable threat about killing a baby mouse. One of Tsarmina's captains suggests torturing a pair of young hedgehogs for information. Ferahgo the Assassin sentences two infant badgers to death by freezing winter conditions. And Swartt Sixclaw- You know what, let's just say that any and every villain in this series would hurt and/or kill and/or eat a child.
Stardoc. Well, let's see: The Hsktskt (or at least, many of them) are the obvious ones. Ktarka Zamlon Torin would have killed Fasala (who was about five at the time)—or at least left her to die—without a qualm; anymember of her adoptive clan was fair game. And then, there's what Joseph Grey Veil did to the male clones.
The Gone series doesn't love this trope—it worships this trope. Just read it. Seriously.
Drake! He kills anyone who gets in the way of what he wants e.g. coyotes-in-daycare scene. Or just gets in his way. Or just for the fun of it.
Everyone villainous in Galaxy of Fear. The kids start off 13 and 12 years old, respectively, and there's no shortage of people willing to do awful, awful things to them.
The books of Roald Dahl often feature adults who make it their jobs to sadistically abuse and taunt children. Even his autobiography about his childhood involves physically violent school teachers.
Musashi contains a rare example of child-killing committed by the main character. After Musashi cripples or kills two headmasters of the Yoshioka School, leadership transfers to a twelve-year-old. A duel is set up between Musashi and the kid "assisted by retainers." Musashi's first move during the duel is to ignore the retainers and rush the kid, cutting him down. Even by mass Values Dissonance of the book, the retainers are outraged by this. Musashi, however, works by his own unique moral code, by which the killing isn't anything he should feel bad about. He comes to regret it later on.
Ryan West's The Rise of the Saxons shows the Anglo-Saxons, while on a genocidal war against the Celts, subject Celtic children to all manner of painful ends: they have their heads smashed in with spiked balls, get impaled on spears, are trampeled by horses, are decapitated, have their eyes gouged out, are skewered while still in the womb and more. And the Anglo-Saxons are the heroes of the novel!
In the NUMA Series book Valhalla Rising, the leader of the villain's death squad attacks a plane being flown by Dirk that was conducting a charity flight for sick kids.
In Les Misérables, the National Guard don't care that Gavroche is a child. They shoot and kill him anyway.
The first book in the Provost's Dog trilogy of the Tortall Universe revolves around the Shadow Snake, a serial kidnapper. If the parents don't pay the items the Snake demands (a book, a necklace, etc), the child dies—and if there are more children, the Snake goes onto one of them. Beka's friend Tansy lost her two-year-old boy this way. And in the third, Tunstall kills one of the young princes.
In Flight To The Lonesome Place by Alexander Key, Anna Maria Rosalita, about 12-years-old, is smacked so hard on her face by her step aunt that she is dazed and has serious bruises days later. The same woman wants to bring her home to the Dominican Republic to a village where the people view Anna Maria Rosalita as a practitioner of black magic and want to kill her.
Also, Ronnie Cleveland, 12-years-old, is running from men who want him dead because of what they think he knows.
Sweet Valley High had a mini-arc involving Margo, a serial killer who resembles the twins and plans to kill Elizabeth and take over her life. She murders her five-year-old foster sister, another child for whom she had been hired as a nanny, and tries to kill a third child she was babysitting.
His Dark Materials: The Gobblers kidnapped children in order to experiment on them by severing their daemons (souls) from them. This usually resulted in death either immediately or within a few weeks.
Mrs. Coulter was said to get unusual pleasure watching the process take place, unless the victim was Lyra.
Lord Asriel used Roger's death caused by spearating him and his daemon to power the machine that opened up the bridge to parallel universes.
The Magesterium, in particular the Consistorial Court of Discipline tried a number of times to kill Lyra starting in the second book.
By virtue of the protagonists of the Goosebumps books always being kids or preteens, nearly all the villains are perfectly willing to harm children — some even make them their primary targets.
In the Rainbow Magic series, Jack Frost has attacked Rachel and Kirsty many times with his ice bolts, once attempting to have icicles rain down on them.
In American Psycho, Patrick Bateman stabs a small boy to death just to see if he'd enjoy it. He doesn't... because he doesn't find it evil enough:
"How useless, how extraordinarily painless, it is to take a child's life... It's so much worse (and more pleasurable) taking the life of someone who has hit his or her prime, who has the beginnings of a full history, a spouse, a network of friends, a career, whose death will upset far more people whose capacity for grief is limitless than a child's would, perhaps ruin many more lives than just the meaningless, puny death of this boy."
Shoteka from Seeker Bears was willing to kill Toklo as a cub all because Oka told him off and then kicked his butt.
The villains in Deep Secret have no problem hurting children—and in fact, they murder several kids who are supposed to be heirs to the multiverse's largest empire. It leaves main character Rupert feeling incredibly ill—and like a a complete failure.
The reactionary right-wing Catholic group Umbra Domini in The Genesis Codeorders the death of 18 children and their mothers.