Sometimes this question will come up. Answer seems simple, right? You fill out a loan, then it's in your name. Since it's in your name, then it's your responsibility. But the question most often comes up because of type of loan as well as the age of the student.
First, the type of loan. If a student fills out a Master Promissory Note (MPN) and loan request for a Subsidized and/or Unsubsidized Direct Loan, then it is the responsibility of the student. If a PLUS Loan is completed, that is the responsibility of the parent. The easiest way to remember that is to remember who actually completed the MPN for each loan. The student completes the Direct Loan MPN, whereas the parent completes the PLUS Loan MPN. Remember that federal Direct Loans do not ask for cosigners, so only the student completes any part of it. Also remember that just because the loan is in the student's name, it doesn't mean that the parent can't help with payment or even pay the whole thing. It just means that the student will be held accountable if it isn't paid back.
Second, the age of the student. The Higher Education Act makes an exception for students under the age of 18 to take on a federal student loan without needing a cosigner even though it is a contract. Why is this relevant? Because of their age. It is legal for a business in most states to enter into a contract with a minor, but it's a dumb thing for the business to do so. Why? Because the minor has the right to back out of the contract and not be held liable. (The exception is if they committed some type of fraud, then most likely they will have to pay restitution.) If the minor had a cosigner, like a parent, then the contract is legally binding for that minor. But with the exception in the HEA, students are responsible for their student loans, even if they are not 18.
Students should always read and study as much as they can about their student loans, especially if they are private loans from a bank. They don't always work the same as the federal loans and usually have a lot more fine print. When in doubt, your best action is to ask questions, either to your loan servicer or your FA office.