Can a 16-year-old move out of her parents' house and live with her 18-year-old boyfriend?

Yes, but the parents of the 16 year old is still responsible for their child's actions. The 16 year old must decide wisely, so that in the future she would not regret her decision. * Not without parental permission. Even with parental permission authorities would have the right to intervene if they so choose. The legal age of majority in almost all US states is 18. In Alabama and Nebraska it is 19, in Mississippi and Washington D.C. it is 21.