Discourse is an open source discussion platform built for the next decade of the Internet. A modern forum, everything's been redesigned to be easy. Self-hosted Discourse software is free, hosting service is paid.
Flarum is free, open-source forum software with a focus on simplicity. You can use Flarum to easily set up a discussion forum for your website. Flarum is developed openly on GitHub. It is the combined successor of esoTalk and FluxBB. It aims to be:
Since its creation in 2000, phpBB™ has become the most widely used Open Source forum solution. Like its predecessors, phpBB™ 3.2 “Rhea” has an easy to use administration panel and a user friendly installation process, which allows you to have a forum set up in minutes.