I don't think I'd move in with my parents. Independence teaches you certain life skills that you won't learn with your parents.
However, if I were to live with them, I'd probably give monthly contributions because I wouldn't want to gobble up their resources, and my parents are supposed to retire soon. I'd give them about $800/month versus $1400/month if I live by myself. That way, I'd still be saving money while providing a little income to my parents.