Are you married? If not, there is no one legally obligated to pay off your student loans or credit card debts unless they are a cosigner on the loans (based on US law). If you have money in the bank, or some of your assets can be liquidated upon your death, those can go to paying towards your debts after estate expenses have been paid. I don't know where you live, but in the US there's a "pecking order" as to who gets paid first when someone dies when there are debts. Firstly, the deceased is entitled to a funeral and burial expenses being paid from their assets. Secondly, ongoing bills such as mortgages, taxes, utilities, insurances, etc, must keep being paid. Thirdly, the court fees for handling the estate must get paid. Forth, the lawyer handling the estate must get paid. Fifth, the "executor" of the estate must get paid. If the decedent has a house that must be sold, the realtor is entitled to be paid. After that, the creditors can share in anything that is left, but it might be unequal sharing, depending on who they are. This all assumes you have any money in the bank and have assets that are actually worth anything and can be liquidated. Obviously, if you have no money, bills will just not get paid and creditors will just be out of luck. If you are married, your spouse (usually) becomes liable for much of your debt. Your children are never responsible for your debt unless they cosigned a loan with you, nor are your parents, or siblings, for the same reason. O course, if you are in a business with your family, or even someone else, your share of whatever debts you have related to that business get passed onto your business partner(s). Now, depending on how you have things set up as far as your bank accounts and such, they can pass directly to someone, bypassing the estate process. This is usually true of "joint" accounts owned by 2 or more people (John Smith AND Sally Jones). If you owe the government money, they can circumvent any "beneficiary" status that you place on accounts, such as a 401K, and basically, just take the money, regardless whether you designated a beneficiary.
I hope you have a will drafted and get any and all of your assets listed in it and make your desires known.