You have to be the age of majority -- 18 in the US -- in order to sign a contract with a cell phone company. A cell phone company cannot legally contract with a minor (under the age of 18). You would have to get your mother or some other adult get the contract in their name and have you added as a authorized user.
As far as having a contract in your own name and being legally responsible for it, you have to be at least 18 years old. Other than that, parents can create accounts for their children at whatever age they feel like.