The answer to your question really depends on your personal situation, and will require specific advice from an estate planning attorney. Although some credit card issuers offer payment protection plans, their benefits often apply to job loss or disability, not for death.
When you die, your estate becomes responsible for paying any debts outstanding to your credit card issuers, your personal lenders, or any other creditors. If you're unmarried, a probate court will likely decide how best to liquidate your assets and distribute any remainders to your heirs based on the instructions in your will. The executor of your estate will facilitate paying out your final balances.
Married couples face some challenges, however. If you opened a credit card in your own name and your spouse is just an authorized user, he or she is probably not responsible for your debt. (I say "probably," because laws vary somewhat in nine states that observe "community property" rules.) On the other hand, when you leave behind a joint account in both of your names, your widow or widower will assume any remaining balance on that account. Establishing a term life insurance policy with your spouse as a named beneficiary can protect them from a sudden crush of debt.
I'm assuming you're asking this question because the value of your estate, if an unfortunate incident occurred to you today, wouldn't cover your current debts. Even though you might not be legally required to repay a debt after your death, many Americans feel a moral obligation to ensure they leave this world with an even balance sheet. Taking a few steps now can also protect your loved ones from unethical or aggressive third-party debt collectors.
Depending on your age and health status, you should be able to find an affordable term life insurance policy that can cover your outstanding debts. An estate planning attorney can help you assign a beneficiary with clear instructions to pay off your remaining balances. In some situations, this could just involve naming your estate as your primary beneficiary, although you'll need to account for probate fees and a stipend for your executor. Other cases may require more complex solutions, such as establishing a trust and writing a very clear will.
Make this process part of a routine financial review you conduct with the help of a fee-based financial planner, your attorney, your key family members, and other trusted advisers. Strong planning now can avoid confusion and frustration for your loved ones later.