A good rule of thumb with bankruptcy law is that unless a debt is specifically excluded, it may be discharged.
The most common exclusions faced by individuals would be:
Student loans – Student loans generally come due and owing after graduation and accrue penalties and interest over time.
Support, separation and divorce obligations – Obligations ordered by a family court may not be discharged regardless of the debtor’s financial circumstances. Only a further family court order can modify such an obligation.
Wages, salaries and commissions – Wages, salaries and commissions paid to employees may not be discharged and can be recovered through suit.
Taxes and certain other debts – Taxes and certain other debts, including government medical expenses, may not be discharged and usually are subject to recovery by government withholding of monies owed until compensated for.
Claims for death or injury while intoxicated – Claims for death or injury while intoxicated may not be discharged regardless of a debtor’s financial circumstances and may be recovered by suit.

Although this list includes the most common exclusions while filing for bankruptcy, it is not all-inclusive. If you have a question about a certain debt that you may owe, you should contact a Bankruptcy attorney in your jurisdiction.