No. Parents are, however, responsible for the Federal PLUS loans. Parents will only be responsible for your educational loans if you are under 18 and they co-sign your loan. In general, you and you alone are responsible for repaying your educational loans.
On the other hand, 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.