Do the banks and creditors you still owe money forgive your debt or do you bequeath your debt to your surviving family along with your precious heirlooms?
The cut and dry answer is this: Your debt belongs to you and you alone; it is not passed on to your family members when you die. The full and complete answer is something only an estate planning expert with knowledge of your state's laws can answer.
In most cases, the only instance in which someone else would be responsible for your debt is if they cosigned a loan with you. By cosigning, both parties assume full responsibility for the loan. If one person cannot pay (for a number of reasons including, but not limited to, death), the other person carries the remainder of the debt alone.
As your estate is settled after death, any remaining debts you owe are paid out from the value of your estate. If your estate doesn't have enough value to cover all of your debts, they will be paid out at equal percentages until the estate money runs out. All remaining debt will be forgiven.