phpBB is a powerful, multi-functional, and easily modifiable bulletin board package. phpBB has a user-friendly interface, simple administration, and helpful tutorial. With phpBB you can:

have unlimited forums and posts
use multiple language interface
search within forum posts
post private messages to your forum members

phpBB and Mambo CMS: phpBB is the most popular open source bulletin board software. phpBB community has provided tools which allow you to integrate Mambo CMS with phpBB and use them both on your site.

Simple Machines Forum (SMF) is free, elegant, feature-rich community forum software. It has a comprehensible and intuitive user interface. SMF has large online community with developers and other users able and willing to help. It has many high-value and high-quality features. SMF offers easy-to-modify theme support and has highly optimized database structure and queries are suitable for small and large forums.

Joomla and SMF - SMF software is the best tool to integrate within your Joomla! CMS design.

vBulletin is a feature-rich, scalable and easily modifiable forums package for your web site. vBulletin is suitable for medium and large forum communities. Being paid software, vBulletin ensures much better security of its code and database. vBulletin is written in PHP and uses MySQL backend.

SiteGround Hosting has chosen vBulletin for its Community Forum software.

Invision Board is a powerful and scaleable bulletin board system. It allows you to easily create, customize and manage your online forum. IPB is written in PHP and needs one MySQL database. It is easily installed, has intuitive administration and tons of features.