Section 523 of the Bankruptcy Code provides a laundry list of situations where a discharge is not allowed. The text of the section is below. The most common exceptions to discharge are:
(1) Child support or other domestic support obligations;
(2) Taxes (although a discharge is possible for taxes under certain circumstances);
(3) Unlisted debts (although these can still be dischargeable in some cases).
Here’s a link to the full text of Bankruptcy Code Section 523