Snow Leopard should be compatible with most applications that ran on Leopard; however, the revamped underpinnings have broken functionality with a few applications. Some of these Apple has been able to identify and the system will notify you of the incompatibility, but others have not worked and either unexpectedly quit or hang.
Apple has a knowledgebase article that outlines the known programs which are either disabled during OS installation or prevented from launching altogether. This list is available here: http://support.apple.com/kb/HT3258
In addition to this list, Wikidot has a page that is being populated with applications that do and do not work on Snow Leopard, which may be exceptionally useful to people considering updating and are not certain of whether or not their applications will run. Do keep in mind that the entries on Wikidot are from one person's experiences so there may be some inaccuracies. The list is available here: http://snowleopard.wikidot.com/