I recently played around with the possibilities of fuzzing. It's a simple way to find bugs in applications.
What you do: You have some application that parses some kind of file format. You create lots (thousands) of files which have small errors. The simplest approach is to just change random bits. If the app crashes, you've found a bug, it's quite likely that it's a security relevant one. This is especially crucial for apps like mail scanners (antivirus), but pretty much works for every app that parses foreign input. It works especially well on uncommon file formats, because their code is often not well maintained.