“Single Parent Rule:” RPG characters with two living parents are almost unheard of. As a general rule, male characters will only have a mother, and female characters will only have a father. The missing parent either vanished mysteriously and traumatically several years ago or is never referred to at all. Frequently the main character’s surviving parent will also meet an awkward end just after the story begins, thus freeing him of inconvenient filial obligations.
The last three words are the kicker - parents, and family in general, are plainly something that we'd like to ditch where it comes to our imaginations. Good thing, too, since Mom probably wouldn't approve of gouging out that goblin's skull and using it and your favorite dagger to play snag-the-eye-socket when things get dull. When I write novels I tend to whack off both my protagonists parents before the story starts, mostly because I don't like my own parents and I'm not interested in creating an ersatz functional family. It helps my characters retain their rugged lone wolf natures, people going it alone with a fuck-you attitude towards others. Much like any group of D&D players.
I pretty much hate family stories, in film or literature, since they tend to be very preachy. RPGs are proof-positive that players believe happiness can be obtained without needing family ... either the one that spawns us, or one we might spawn. I offer this piece of advice, as something the gentle reader should never do as a DM: if you want to curse a female character in a party, make her pregnant. The player will not be amused. And that, dear friends, is a social commentary on many, many levels.
(I did have a player who did get married, and did have children, and the campaign running long enough for that player's children to grow into young adults. But this is extraordinarily rare in my experience).
In recognition that we in western society clearly hate our parents and will happily identify with orphans and abandoned children in film after film, have a look at the truly impressive list of children's stories, from Disney, Pixar and Don Bluth, where parents are non-existent or clearly an afterthought. This goes on and on, in live action children's films as well as animations ... we are programmed from the age of four to fantasize about discarding our parents. Why, look at the three great children's stories of English literature: Peter Pan, the Wizard of Oz and Alice of Wonderland.
Adventure begins when the parents are gone.
That's really all I have to say on the subject. I can hardly encourage players to think more about their imaginary mothers and fathers, now can I? Who would, anyway? I mean, unless your father is the King of the Land ...
But then a thought does occur to me. What would anyone say to a starting adventure for a party being the intentional murder of the character's rich, wealthy parents, in order to usurp the family business, or merely to obtain for themselves a nice compensation. Yes, that's right Marvolo ... your father is rich, very rich, and he has been a bastard to you all your life - your mother too! Don't you remember, your mother killed your dog Rex ... and fed his to the corpse to the pigs? For ten years, you've hated them, despised them, thought of all you could do with their money. And now today, this very morning, your master has declared there's nothing else he can teach you. Today you are a first level thief!