Can all types of debt be discharged?

No. The debts that can't be discharged vary slightly between the different chapters of bankruptcy. Generally, the following cannot be discharged:
o Debts for taxes owed to local, state or federal agencies (but there are important exceptions to this!)
o Debts for money, property, services, or an extension, renewal, or refinancing of credit, which was obtained fraudulently
o Debts that weren't in the initial list of debts or that the debtor waived being cancelled
o Debts owed to a spouse, former spouse, or child, for alimony, maintenance, or support of a spouse or child, with a separation agreement, divorce decree or other order of a court of record
o Debts owed for injury to another person or property owned by another (as in a court judgment)
o Debts for any educational loans, unless it can be shown that repayment will cause an undue hardship
o Debts for death or personal injury caused by the debtor's drunk driving or from driving while under the influence of drugs or other substances (as in a court judgment)
o Debts incurred after a bankruptcy was filed
o Any type of criminal fine or restitution