Vampire: The Masquerade does this as part of its "Personal Horror" philosophy. Being killed by some supernatural monstrosity is the least of your worries. Vampire society is essentially based around family units, and the moment you receive the Embrace, youíre inextricably linked to your new family. Unfortunately, your vampire dad is likely to be an Abusive Parent, which you can do nothing about because Kindred society happily tolerates such behavior and brutally punishes "ungrateful" childer. If you do manage to flee your Sireís grasp, your extended family (read: your Clan) likely has dozens more of the sort who WILL force you to deal with them. Even outside the family, everyone is constantly watching for weaknesses in everyone else. Accidentally said the wrong thing to the wrong person? Maybe nothing will come of it. Maybe someone will burn down your house while you sleep. Or maybe they will let you go insane with paranoia for the next few years, THEN burn down your house while you sleep. Needless to say, anyone and anything you love can and will be used against you. Your mortal family is a valid target. And if you create a ghoul or childe of your own to make existence a little easier? Congratulations, now you not only have to keep yourself out of trouble, but all of them, too! And did we mention that everyone is experiencing a slow Descent into Addiction, which comes with a Hair-Trigger Temper to boot, practically enforcing Poor Communication Kills? Itís no wonder many fledglings choose to walk into the sun with a "family" that dysfunctional.
Even Pentex gets into the game with their Avalon Toys subsidiary, which subtly broadcast messages to kids about the importance of violence, the necessity of staying thin and pretty to remain popular, and the fun of "playing" veterinarian with stray animals. Such messages leave kids attuned to the memetics of the Wyrm and thus ripe for possession by Bane spirits. So even if you're out fighting tooth and claw against the forces of evil, there's still a chance they can get to your kid when you're not around...
Little Fears is a roleplaying game that plays on this just as much as it does childhood fears. Your children stand risk of being killed - or worse - by an enemy that's ever-hungering, comes in many forms, and is completely invisible to you. It may have even gone after you, too; you just forgot all about it when you reached puberty.
In the kingdom of Bretonnia in Warhammer, the standard policy of the local religion, the Cult of the Lady of the Lake, is to track down children with magical potential and take them away to an undisclosed location for their own safety and for the safety of the kingdom - the cult is highly secretive. Some of the girls come back as priestesses of the Lady (of course they also refuse to comment on where exactly they've been) while the boys... well, they're pretty much invariably never seen ever again. Bretonnia is pretty much an awful place to live, but especially if you're a parent.
The Wood Elves are known for kidnapping human children from Bretonnia and turning them into ageless slaves who will gradually forget their families and think the elves are their masters., Some are captured during the elves annual wild hunts, others are taken in the night, and some are lured into the forest. It's even implied that the Cult of the Lady take children with magical abilities to Wood Elf realm of Athel Loren and present them as slaves to the Elves since the Elves are implied to be behind the Cult of the Lady. Bretonnian parents must be worried about their children 24/7.