Here are 7 Perl, open-source & free forum Appliances, where most of them are built with PHP, that you may consider using. They can be easily integrated into a website by customizing the look & feel or used as a framework which is sometimes a good idea considering the features they offer.
1. MyBB - MyBB has nice features like calendar/events, mass mailing to members, a built-in theme editor & more.

2. Discuz! | Download Discuz! 7.0 English Full | Demo | Admin Username: admin, Admin Password: admin
Crossday Discuz! Board (or simply Discuz!) is an Internet forum developed by Comsenz Technology Ltd. It is built on the PHP scripting language, supporting MySQL and PostgreSQL database management systems. Discuz! is free for personal use. A commercial license costs 3000 renminbi. The newest version of Discuz! Board is Discuz! 7.0. It is now widely used in China and Hong Kong, but has not been very popular in other countries/places due to lack of support for other languages. The latest English version of 7.0 is developed by 3rd party and preview edition released.
