Not all debts are discharged. The debts discharged vary under each chapter of the Bankruptcy Code. Section 523(a) of the Code specifically excepts various categories of debts from the discharge granted. Therefore, you must still repay those debts after bankruptcy. Congress has determined that these types of debts are not dischargeable for public policy reasons (based either on the nature of the debt or the fact that the debts were incurred due to improper behavior of the debtor, such as the debtor's drunken driving).
The most common types of non-dischargeable debts are certain types of tax claims, debts not listed by the debtor on the lists and schedules, debts for spousal or child support or alimony, debts to governmental units for fines and penalties, debts for most government funded or guaranteed educational loans or benefit overpayments, debts for personal injury caused by the debtor's operation of a motor vehicle while intoxicated.