I asked my mom, who works for social services, and here's what she says:
You can have your own biological children sleep anywhere you please at any age -- the living room sofa is perfectly legal. You have to provide heat, electricity, etc., but privacy is not a requirement.
If you have a foster child, he or she may share only with other children of the same gender. Also, a foster child must have a permanant bed (i.e., not a pull-out sofa or a blow-up mattress).
Realistically, since it's so hard to find a child who's available to adopt, a family who can't provide a private room won't have a chance.
Finally, an individual or an apartment complex can decide what it will and won't allow on its property. If they choose to say that you can't have children sharing, they can make a rule.