An Internet forum, or message board, is an online discussion site where people can hold conversations in the form of posted messages. They differ from chat rooms in that messages are often longer than one line of text, and are at least temporarily archived.

AEFs full name is Advanced Electron Forum. This bulletin board software is free software. It is written in PHP and MySQL. AEF has a very simple and easy to use Administration Panel and installing this software is a piece of cake! You can install new themes, customize themes the way you want. The User Control Panel has a simple yet beautiful interface where users can set their preferences for the board. This Bulletin board or forum software has all the general features that a forum software should have. Yet it is so Fast!
bbPress is forum software with a twist from the creators of WordPress. bbPress is plain and simple forum software, plain and simple. It’s easy to use, easy to administrate, fast and clean. But don’t let its simplicity deceive you; underneath the gleam, it’s got some powerful features and is highly customizable
Beehive is an online forum/message board system with several powerful features. Beehive is an open-source project for creating a high-configurable frame-based discussion forum. Almost every aspect of Beehive is customisable to some degree, from the forum's name right down to how many posts per page each user wants to see, and with everything inbetween, including guest accounts, user profile catagories, your start page, your top frame, user's signatures, language packs, forum styles and emoticon sets - and if you don't like those that come as standard, it's easy to create add your own!
Carbon Forum is a topic-based high-performance lightweight PHP forum.
ElkArte is a modern, powerful community building forum software. It is created by volunteers who believe in freedom of software. Initially based on Simple Machines Forum (SMF), it began with a complete overhaul of the code in order to modernize, implement new features and make a forum software be relevant in a time of unprecedented social interaction. It has grown to become a modern, feature rich forum package to meet the demands of today's discussion groups.
FluxBB is a free open source forum application designed to be fast, light and user friendly. FluxBB's code, written in PHP, has a proven track record of stability and security. FluxBB is being actively developed.
FUDforum (Fast Uncompromising Discussion Forum) is a free and open source web discussion forum. FUDforum combines an extensive feature set while maintaining the ability to generate forum web pages extremely fast. The forum includes i18n and templating support allowing for a complete customization of its output as well as a very capable group based permission system. FUDforum can also act as a Mailing List Manager, USENET newsreader and even an XML Feed Aggregator. This will allow you to build an instant community and consolidate all your messages into a single system.
LayerBB is a small yet feature rich community software which enables you to quickly and easily start your own community. It offers great flexibility and easily customisable.
miniBB is a standalone, open source program for building your own Internet forum. If you want a lite, simple and stable message board attached to your existing website at the very high integration level, which may include the full customization of the layout to the look of your website, or even synchronizing with the existing membership system, you've just came across to the best forum solution for such purpose available worldwide.
my little forum is a simple PHP and MySQL based internet forum that displays the messages in classical threaded view (tree structure).
MyBB is a free bulletin board system software package developed by the MyBB Group. A lot of thought has gone into the MyBB interface to make it easy to use. MyBB uses a standard discussion board structure, so your visitors will feel familiar with the way MyBB works. Your visitors can use the MyBB user control panel to change the way they view discussions. They can also easily start and reply to discussions and markup their posts. The forum administrators and moderators can use MyBB's inline editing and moderation features to control discussion and keep the forum tidy.
Phorum was the original PHP and MySQL based Open Source forum software. Phorum's developers pride themselves on creating message board software that is designed to meet different needs of different web sites while not sacrificing performance or features.
phpBB is used by millions of people on a daily basis, making it the most widely used opensource bulletin board system in the world. Whether you want to stay in touch with a small group of friends or are looking to set up a large multi-category board for a corporate website, phpBB has the features you need built in. Newer users will appreciate phpBB's extensive administration panel, which allows the customization of even the most intricate features without having to edit code directly, while advanced users will value the ease with which phpBB can be integrated into existing systems.
PunBB is a fast and lightweight PHP-powered discussion board. Its primary goals are to be faster, smaller and less graphically intensive as compared to other discussion boards. PunBB has fewer features than many other discussion boards, but is generally faster and outputs smaller, semantically correct XHTML-compliant pages.
SMF in short is a free, professional grade software package that allows you to set up your own online community within minutes. Its powerful custom made template engine puts you in full control of the lay-out of your message board and with our unique SSI - or Server Side Includes - function you can let your forum and your website interact with each other. SMF is written in the popular language PHP and uses a MySQL database. It is designed to provide you with all the features you need from a bulletin board while having an absolute minimal impact on the resources of the server. SMF is the next generation of forum software - and best of all it is and will always remain completely free!
TangoBB is a project for a new and simple bulletin board. Bigger improvements, better experience. Continuing to create a forum software that is easy to use.
Unclassified NewsBoard (short UNB) is an open-source, PHP-based internet bulletin board system, mostly like those you may already know. But the difference is in a lot of details that make your life with this board, both as administrator and user, much easier. You'll be surprised how easy things can be and how fast you can work with such a system!
Vanilla Forums are open-source, standards-compliant, customizable discussion forums.

It is specially made to help small communities grow larger through SEO mojo, totally customizable social tools, and great user experience. Vanilla is also built with integration at the forefront, so it can seamlessly integrate with your existing website, blog, or custom-built application.
XMB
XMB is a lightweight PHP forum software with all the features you need to support a growing community. With outstanding community support and contribution, you will find XMB to be easy to setup, customize, and enhance.