For a long time in western civilization it was customary for kids to be given their father's last name, due in part to the patrilineal lines of succession and inheritence of the times.
Nowadays, though, it is becoming increasingly common that women retain their maiden names rather than take their husbands, which I suspect would cause some confusion about what the two should name their children.
I've heard of having male children take their father's name and the female ones take their mother's, but I have also been told that more than a few families would prefer that all of their children have the same last name.
I've also heard of taking the mother's and father's names and hyphenating them, which is all well and good for one generation, but seems a little unrealistic in the long-term if widely adopted. For example, Mr. Francis and Mrs. Johnson have a son, Mr Francis-Johnson. He then goes on to have a child, named Mr. Francis-Johnson-Micheals-Brown, who then fathers Mr. Francis-Johnson-Micheals-Brown-Smith-Joseph-Lee-Chan.
So how would you decide on your kids' names? Just adopt the father's name, same-sex parent's name, hyphenated name, or some other solution I didn't think of?