SEO-Board is a forum software that's fast, free, and search engine friendly. It is the perfect solution for small and medium-sized sites.

Features:

Written in PHP and uses MySQL as a back-end. Requires: PHP 4.3.0 and MYSQL 3.23.23.
No bloat. No fancy features. Just blazing speed.
Does not take too many server resources.
PHP and HTML are separated for ultra easy customization.
Is flexible. Can fit into your site design.
Anti-spam protection. Admin can ban IP/IP ranges/Users/Emails.
Full moderator support.
Message preview; locked and sticky topics; new topics highlight.
Search Engine Friendly: comes with Apache mod_rewrite support; cookie-based sessions (no SessionIDs in the URLs)
Multi-language pack support.
Support for Private, Read-Only, Post-Only, Guest, HTML-Allowed, Topic Creation-Time Sorted Forums.
Basic BBCode, Smilie, Signatures and Avatars support.
Support for RSS/Atom feeds
Forever 100% free for both personal and commercial use.

Listed in Forums php scripts category