A blanket note for several of the examples below: While it's hard to confirm because the ESRB criteria for rating games isn't entirely transparent, a number of people have alleged that allowing the player to deliberately murder children in a game is a fast track to an Adults Only rating; this would be financial suicide for any title with a multi-million budget as all major consoles prohibit AO titles on their system and few retail stores (and no major ones) will carry them. (This may have carried less weight in the 90s, especially for PC games which got lax treatment to begin with.)
The PC frees the inmates of an asylum for those driven mad by magical power to help take on Big Bad Jon Irenicus. One of these inmates is a young girl with the ability to shapeshift; she does not actually take part in the battle, in which all the other inmates die.
Castlevania 64 has the hero fighting horrible menaces to save a human kid named Malus. Then he sends him off into the monster-filled worlds. The rerelease had a different hero give a different kid a plot coupon that would protect him from said monsters.
Subverted in Malus' case since he's freaking Dracula reborn. In the true ending you get to confront and kill him.
No children or infants appear in the Crusader series of games, because with the care most players usually take to avoid killing civilians there would be frozen, burning, or gooey babies everywhere. And you can't get baby out of carpet.
In Dragon Quest V, during the segment where your characters are children, they don't die when they hit 0 HP, but are just knocked out until the end of the battle. Actual — if not-permanent — death isn't an issue until your lead character is an adult.
Subverted with the PC's own children who CAN get killed in battle
Fable: The only children to appear are in a town which the player cannot enter without leaving his weapons at the gate.
You are never unarmed in Fable II, but no matter what you use, you can't kill the kids. Oddly subverted in the intro sequence, in which Lord Lucien shoots dead your sister Rose, who is barely older than you are, and then shoots you with enough force to send you through a window and down a fall you only survive because of your magical heritage. Near the game's ending, Lucien will kill your spouse and children, offscreen.
In 60 Seconds!, when one of the adults go too long without a needed resource, they die. If a kid goes without food or water, however, they "run away".
Bethesda invokes this trope whenever their videogames have child NPCs. In both Fallout 3 andSkyrim children are completely invincible. Attacking them won't lower their health at all. This is done to prevent these games potentially being used as child-killing simulators, which would most certainly invoke the ire from Moral Guardians. Bethesda is very strict with this policy, as they forbid any discussion about this subject on their forums, while also allegedly removing Youtube videos showcasing mods that allow players to kill children.
In Fallout 3, this restricts an Evil player's options in Little Lamplight, a town populated entirely by kids. While children are invulnerable to harm, a "creative" player will discover that you can enslave some, sell drugs and guns to them, bully them, taunt one to run away from his neglectful mother and the evil solution to the "The Power of Atom" quest (detonating the atomic bomb) will kill the two children living in Megaton.
It's actually still played straight during "The Power of Atom." If you activate the bomb but do not detonate it, leave town, and come back before you finish the quest, you'll find that the two children in Megaton have mysteriously vanished.
Fallout: New Vegas picks up this policy from its predecessor. The game makes a point of this feature by including a quest where one can find a range finder in order to use a prewar super weapon, the ARCHIMEDES II. However the player character needs to obtain said rangefinder from a child named Max who believes that it a toy. Max can not be killed in order to get the rangefinder off of his body, you must pay him a thousand caps (20 with a high barter skill), or pick pocket him. However Max constantly runs so it is impossible to pick pocket him unless he is asleep.
Skyrim is actually inconsistent with this trope. While living children are invincible, there are two undead children in the game, them being Helgi and Babette. Helgi is a ghost of a girl who died in a fire, while Babette is a Really 700 Years Old vampire and an assassin of the Dark Brotherhood, who was turned into a vampire at a very young age, meaning both cases avert Infant Immortality. But if the player raids the Dark Brotherhood sanctuary, Babette is nowhere to be found, as to prevent the player from killing a child, despite said child being a self proclaimed three hundred years old killer.
This is applied strangely in F.E.A.R. Alma is already an Implacable Man, but the moment you have to actually face off against her, she goes from her Creepy ChildStringy-Haired Ghost Girl form to a teenage one. This makes absolutely no sense plot-wise, and seems to be solely so you won't have to face down and eventually shoot a little girl — even one that's already dead.
It does make sense in the way that Alma is actually grown-up, since she already gave birth to the player character. Thus, you see her "real form" instead of the mind-projection of a little girl.
Canonically, she was an adult when she died — but, IIRC, only fifteen when she gave birth — but she was unconscious nearly the entire time, and would have no frame of reference for herself looking like this. It doesn't make a lot of sense that she'd psychically project herself as what is, to her, virtually a complete stranger, rather than the image she probably has of herself.
There's also the small matter of Alma raping the main character at the end of the second game. Doing that while she still looks like a little girl would probably cause even worse publicity than being able to shoot her.
In Final Fantasy Fables: Chocobo's Dungeon, the journey into people's memories starts by chasing a mysterious flying infant, worried that he'll be hurt. He somehow manages to escape the monsters unscathed, though Chocobo has a hard time finding his way through.
Grand Theft Auto: In a game where you can beat people to death, blow up cars, and just be an all around psychopath, there are no kids and it also regularly Lampshades the absence of pets. Averted in Grand Theft Auto V where it has people walking their dogs and you can kill the dogs for no reason other than to be a complete jerk. Attacking the owners or causing general mayhem will have the dogs attack you and they can One-Hit Kill you if you're not careful. Going into the wilderness will have you encounter deer, coyotes, and rabbits, all which will actively run away from you if you spook them, but cougars will attack you the moment you're spotted by them.
The reason why there aren't any children in Half-Life 2 - so they can't be killed. The game designers turned it at their advantage though: the childless city was explained in-game by a "suppression field" which prevents certain protein chains necessary for embryonic development from forming, according to Doctor Kleiner. There's a great atmospheric moment at the start of the game, when you pass by a playground and, if you look at the deserted swing and the broken doll on the ground, you can hear a distant, fading kid's laughter.
Amusingly lampshaded once the suppression field goes down - Kleiner suggests via broadcast that, while the Citadel's reactor is going critical, "now would be an excellent time for procreation" for those who are out of the city.
Depending on which games in The Legend of Zelda series and how good the player is, this can either be played straight or subverted with a child Link.
In The Sims 2 and The Sims 3, babies and toddlers cannot be killed in any way. If they are caught in a fire they will miraculously escape, and if their needs drop too low, a social worker will take them away. The same is true for children, except they actually can burn to death, drown, or get crushed by a satellite or meteor. They just can't get electrocuted, scared to death, or starved to death (the social worker will come first). Pregnant women also cannot die. However, ghosts in 3 can reproduce (with other ghosts or with living Sims), and the babies are sometimes ghosts who will then age like normal Sims.
This is in full swing in the Siren series... which actually works against the player, as they enforce it by having children panic and curl into a ball before they're actually even hit, yielding a game over. If you're playing one, you're currently playing a stage where not using stealth, rather than just being dangerous and wasteful, is completely impossible. If you have one with you, you have to take great care to protect it — and a stray hit during combat that connects with them causes them to panic as well.
Both an example and exception in Siren: Blood Curse. On escort missions, you can hurt and kill the person you have to protect. Except 10-year-old Bella. Your weapon has no effect on her. Likewise, enemies can hurt and kill escorts... but when Bella "dies" it's by covering her head and cowering in fear. And when you play as Bella, instead of taking damage from enemy attacks and eventually dying, you cower in fear and scream "NO!" if an enemy gets too close to you, causing you to lose. Technically a way of avoiding showing Bella's obvious death. Yet, the game also creates an exception later when Bella is shown later on having turned into a shibito, the zombie-like creatures in the village. The condition for becoming a shibito is to die, so obviously something happened to Bella. An earlier cutscene shows a large log rolling towards her and a quick cut to black, indicating that's what might have killed her.
Tails from Sonic the Hedgehog cannot die if you play as both Sonic and Tails in Sonic 2 and 3.
World of Warcraft follows this to a T. You can slaughter whole towns, but not the children in them. Apparently it's better to let the children get along without their parents that you slaughtered than to also kill them. Then again, given respawn, that's not an issue...so it raises the question of why one can't kill a level 5 child since they'd just come back anyway.
The reason is, Blizzard doesn't want either side to seem Always Chaotic Evil to the other, and child murder is a good way of crossing the Moral Event Horizon. This is also lampshaded with an in-game holiday dedicated to helping the orphans in every city.
Averted somewhat lore-wise, given the presence of NPCs such as Pamela Redpath.
Even then if an undead child has to be depicted, they have to be depicted as that of a ghost. So yeah, no zombie kids for Children's Week.
It's only to be expected that Zoo Tycoon would honor this trope, being a family game. It's worth mentioning because of how blatantly the Infant Immortality rule is applied: if predators escape or a guest ends up in their enclosures, they'll leap on and attack adult guests, while completely ignoring children. Hence, a runaway lion or tyrannosaur will charge right past a dozen kids to pounce on a grown-up.
The Sonic Blast Man arcade game (as well as the SNES version) featured a stage where the player must punch out a truck that is about to cross path with a runaway carriage with a baby boy inside it. If the player fails the stage, it will show that the carriage managed to get safely out of the truck's way, only for Sonic Blast Man to get run over in its place.
However averted in a battle of Shining Force III where three of the five refugees you're tasked with saving are children, they have the lowest hit points in the group so the enemies will target the children over the adults. And yes, you are treated to a 3D cinematic of enemy knights slaughtering helpless civilian children.
In Virtue's Last Reward, Quark is the only person you will never explicitly see dead. Everyone else is fair game.
Though it is highly unlikely he survives any of the endings where the whole facility goes up in an explosion.
In Final Fantasy XII, you will occasionally be joined by a fourth party member. The only guest party member who doesn't eventually die is Larsa, who is twelve.
In the Japanese version of Scribblenauts, child NPCs have infinite hit points.
In Nira Oni, a group of teenagers gets trapped in an Abandoned Hospital. Although they're all in danger, most of the cast show particular concern about Cassey's younger sister Ryan, and this directly factors into the ending. Hiroshi can decide to ensure she escapes at any cost, meaning she survives even the worst ending... but at the cost of everyone else.
In Terraria, the Angler is the only child in the game. He can be hurt by monsters or traps like the other townsfolk, but instead of dying bloodily like the others, he vanishes in a puff of smoke with the message "[name] has left" when his health runs out. Since this is how some phantasmal enemies like the Wraith "die," the most popular explanation is that he's a ghost, so whether this is an aversion or not is unclear.
The Walking Dead plays with this trope, as while a certainly number of child characters die in horrible ways or are shown undead, a number of them also survive such as Clementine, Alvin Jr. and Sam's brothers in the Michonne spin off regardless of the player's choices.
In Trauma Team, Alyssa takes a bomb blast at point-blank range. The same type of bomb has already been used to kill 4 adults. Not only does Alyssa survive, she even retains all her limbs (the bomb did mangle her quite badly, but she eventually makes a full recovery.)
NARC is a famously violent game where you ruthlessly massacre hundreds of people. But killing dogs, even vicious attack dogs, is evidently considered too violent: in most, if not all ports of the game, shooting or blowing up a dog merely turns it into a puppy that runs away.
Dishonored: While you hear horrible stories of people dying from the Rat Plague (including children) regarding the game world's backstory, the only child you actually meet during the whole game is Emily, and unlike every other NPC in the game, nothing you do can harm her. Subverted at the end of a High-Chaos game, however, as Havelock will attempt to jump from the lighthouse taking Emily with him, and should you screw up, he succeeds.