slash is a database-driven news and message board, using mod_perl and MySQL.
UseBB is an easy-to-set up and easy-to-use Open Source PHP/MySQL bulletin board system with several user and administration possibilities, especially designed for small to medium sized Web sites which do not need the overdose of features found in other forum packages.
vBulletin is a powerful, scalable and fully customisable forums package for your web site.
VIF (virtual discussion forum) is a forum application. VIF is intended for a structured discussion, starting from a high level problem that is refined in subsequent steps until a granularity is reached that allows the questions to be answered.
vtiger Forums is a high powered, fully scalable, and highly customizable Open Source bulletin board package developed over phpBB. The vtiger Forums has a user-friendly interface, simple and straightforward administration panel, and helpful FAQ.
W-Agora is a web-based and customizable forum package. It allows you to install forums, BBS, guestbooks and all derived things.
WBB IRC Postbot
Postbot is a hack for the Woltlab Burning Board (WBB) that posts new threads, posts, and registrations automatically into IRC.
(commercial) WowBB is a PHP/MySQL powered bulletin board. It is designed from the ground up to provide the most functionality with ease-of-use.
X.Forum is a forum using text as the database.