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

http://www.law.cornell.edu/uscode/usc_sec_11_00000523—-000-.html.