Vanilla Forums

Vanilla Forums is an open source self hosted forum software as well as a paid hosted option. It has become a popular community software application as it has concentrated on the core of its business as a community software application. It is a Canadian company and was voted as the top forum software application by CMS critic.
Some popular examples of companies using Vanilla for their community include, Thexyz.
Getting started with Vanilla Forums
You can download the package and install it on your domain for free. It has a simple installer process and requires a MySQL database. There is also a very well put together migration tool of you are coming from another forum software application.
Here at ScriptDorks we tested the migration tool from a phpbb forum and it was impressive how it kept all the posts and setup redirects to the new vanilla URLs. Vanilla has a much improved SEO friendly URL structure than phpbb.

phpBB

phpBB is a fast, efficient discussion board program built in PHP with a muti-database backend. Features include: posting, replying, private messages, polls, username/ip banning, strong encryption for storing passwords, user rankings, very advanced access control for private forums, full templating, simple yet robust translation system and much more.

Visit publisher site: phpBB

Moodle

Moodle is a course management system for producing high-quality Internet-based courses that promote connected knowing and meaningful collaboration. This Open Source application offers a Free alternative to commercial software such as WebCT and Blackboard. Written in PHP, it runs on Linux, Unix, Windows, Mac OS X or Netware 6, using MySQL or PostgreSQL. Courses are easily built up using activity modules such as forums, chat, journals, quizzes, surveys, assignments, resources, choices, glossaries, lessons and workshops. Moodle has native support for easily displaying multimedia including Flash, MP3, video etc. The interface can be used in over 70 native language translations. New languages, plug-in modules and CSS-based themes are being actively developed by a growing community. See our site for details.

Recommended Moodle Hosts:

Oxwall Community Software

Oxwall is free flexible and easy to use PHP/MySQL community software platform. This software is a best decision for a social network website, customer feedback/survey/general community, collaboration tool, family website, photo/video/rich media content sharing website and so much more. Oxwall is built on popular PHP/MySQL technology which means wide and easy adoption in the web-development world. We aim at attracting freelance developers and companies to offer commercial services for Oxwall.Key Features: Full clusterization support for multi-million userbases, modular structure to choose site features like blogs, forums, photo, video, etc., seamless integration with existing database of users, solutions ranging from free hosted 5-minute-to-setup sites to enterprise standalone or existing-site-addon implementations.