Will all debts that were incurred before I filed bankruptcy be discharged in a Chapter 7?

Not necessarily. There are a number of types of debts that are excepted from the discharge received in Chapter 7.  Among the most common debts that will survive after the bankruptcy are debts for child support and alimony; student loans (unless it would be an undue hardship for you to repay); fines and penalties imposed for violating the law, such as traffic tickets and criminal restitution; recent income tax debts and most other tax debts; and debts for personal injury or death caused by driving while intoxicated. Also, debts secured by real or personal property that are reaffirmed in the bankruptcy process are not discharged.
In addition, some debts (fraudulent credit card debt, for example) may be declared nondischargeable by a bankruptcy judge in Chapter 7 if the creditor challenges your request to discharge them.
A debtor with these kinds of debts can still receive a discharge of other debts, but will still owe the “excepted” debts after the bankruptcy.  Additionally, Chapter 7 debtors who engage in certain misconduct connected with the bankruptcy (like failing to disclose assets) may be denied a discharge entirely.
It is important to discuss all your debts with your bankruptcy attorney so that possible non-dischargeable debts can be identified and potential problems can be averted.