phpBB is one of the most widely used forum script currently on the web. It is free/open source, easy to install and administer and allows flexibility in terms of design and organization.
phpBB supports the notion of users and groups, file attachments, full-text search, notifications and more. Hundreds of modifications are available including themes, communications add-ons, spam management and more. Features of phpBB include support for multiple database engines (PostgreSQL, SQLite, MySQL, Oracle Database, Microsoft SQL Server), flat message structure (as opposed to threaded), hierarchical subforums, topic split/merge/lock, user groups, multiple attachments per post, full-text search, plugins and various notification options (e-mail, Jabber instant messaging, ATOM feeds).