In European Union, different member states have different practices. Germany and South European countries have laws and strong social norms that adult children must take care (or at least pay) for caring their old parents. Northern Europe does not (Nordic countries, Netherlands, Belgium, I understand Britain as well).
According to [0], 28 U.S. states make adult children responsible for their parents if their parents can't afford to take care of themselves.
In Russia, law also requires adult children to care for their parents (this I know for a fact due to an immigration case where I helped).
In China caring for old parents is an important responsibility of children, but I do not know how that is formulated in law.
[0] http://www.elderlawanswers.com/requiring-adult-children-to-p...