There are many options, of which the most poplar would be
phpBB2, which is a security nightmare of it's own accord, or
SMF, which is pretty damn nice.
Although it's had problems in the past, if you're not adverse to writing a few lines of PHP code yourself,
MyLittleForum did have
one or two security issues, which is easy to repair (make $lang a global define(LANG,eng); and do a global replace), and the v2 beta. It is a capable system, and it has a 'bad word list' filter as well as a few other plugins. This one will require a little bit of work, though, and v1.7 is NOT Smarty enabled so you will need to write subroutines to do things such as displaying banners.