My parents took out a student loan, but I'm now an independent taxpayer making the payments. Who can claim the interest deduction, me or my parents?

Neither you nor your parents are eligible for the deduction in this unfortunate "catch-22" situation. Even though you are making the payments, you did not take out the loan and do not have primary responsibility for repaying it. Your parents are not eligible for the deduction because they did not pay the student loan interest. Always remember that it is the taxpayer's responsibility to figure and claim the Student Loan Interest Deduction correctly.