No. Parents are, however, responsible for the Federal PLUS loans. Parents will only be responsible for your educational loans if they co-sign your loan. In general you and you alone are responsible for repaying your educational loans.
You do not need to get your parents to cosign your federal student loans, even if you are under age 18, as the 'defense of infancy' does not apply to federal student loans. (The defense of infancy presumes that a minor is not able to enter into contracts, and considers any such contract to be void. There is an explicit exemption to this principle in the Higher Education Act with regard to federal student loans.) However, lenders may require a cosigner on private student loans if your credit history is insufficient or if you are underage. In fact, many private student loan programs are not available to students under age 18 because of the defense of infancy.
If your parents (or grandparents) want to help pay off your loan, you can have your billing statements sent to their address. Likewise, if your lender or loan servicer provides an electronic payment service, where the monthly payments are automatically deducted from a bank account, your parents can agree to have the payments deducted from their account. But your parents are under no obligation to repay your loans. If they forget to pay the bill on time or decide to cancel the electronic payment agreement, you will be held responsible for the payments, not them.