What forms you mean? About composition, well, some families have same sex parents and some have still the traditional form which is heterosexual partnership among parents. Although as the society becomes permissive there is a rise in same sex parents.
Families are leaning toward nuclear families meaning, it is composed of a father and a mother, plus the children - more predominant in western societies. In some societies, there are still extended families where families stay in one household unit including grandparents etc.
The rise in single headed household is increasing as women become more independent and employment opportunities which make them stand on their own.