The general rule is that spouses are not responsible for each other's debts, but there are exceptions. Many states will hold both spouses responsible for a debt incurred by one spouse if the debt constituted a family expense (e.g., child care or groceries). In addition, community property states will hold one spouse responsible for the other's debts because both spouses have equal rights to each other's income. Also, you are both responsible for any debt that you have in both names (e.g., mortgage, home equity loan, credit card).
The 360 Degrees of Financial Literacy Web site offers general information for managing personal finances and does not recommend specific financial actions. For financial advice tailored to your situation, please contact an expert such as a CPA or a personal financial advisor.