There is no set age limit, it is determined by individual persons.
You are however, responsible for your children until they are 18 if they are left unattended.
In my town here, there is a class that children can take that helps them learn how to be babysitters...The class is for children ages 10-13.
It just depends on the child, and their maturity level. If social services were called on a child left alone, they would most likely quiz the child on what to do in emergencies, how to contact parents and other adults etc...If they child has been taught all this they should be alright.
I have a 10 yr old that stays home by himself. He's not quite mature enough to "babysit" other children, but he is mature enough to take care of himself. And I may add, he has learned alot and matured emensely from being able to be home alone.
To sum it up, it's based on the children and their family