To follow my previous post on what happens to your individual debts when you die, this post will speak to joint debts and debts that are guaranteed by a third party (parent or spouse, most likely).
Joint debts, and those guaranteed by a third party, will survive you. Since there is a second party obligated to the debt, your death will not impact the life of that debt, as long as the co-signer or guarantor has not predeceased you. This can be a substantial change in circumstances for your guarantor. If you've been making your student loan payments each month since you graduated college (or law school) and your parents (for example) have to all-of-the-sudden pick up that debt service immediately after your death, that can be a serious strain on cashflow.
What's worse, some student loan companies are treating the death of the borrower as a default on the note and calling the full remaining value of the note immediately. All other debts that are held jointly, the joint credit card, for example, will continue on unchanged.
Proper Estate Planning can protect your assets from your creditors (again, to be continued).