I am a law school graduate. What I offer is mere information, not to be construed as forming an attorney client relationship.
Off the top of my head:
1. Over 18 -- no longer under mom and dad's authority unless you live with them/going to college and they still claim you as a dependent.
If such is the case (they claim as you a dependent) and you are going to school, apply for loans and cards in your own name. Cancel everything you have with them (address, possible shared family cards--take your name off) and that is that.
2. If under 18 -- emancipation-- which takes a very long time and difficult process.
Hope this helps.