I really like WoltLab, they have a great Forum and the community is generally really nice The customer support is also awesome
XenForo - Intuitive. Social. Engaging. Fast. XenForo brings a fresh outlook to forum software.
Discourse - Discourse is an open source discussion platform built for the next decade of the Internet.
phpBB - Raspberry Pi. The Raspberry Pi is a cheap, credit-card sized computer. The official website uses phpBB for their discussion forums. phpBB is not affiliated with nor responsible for any of the sites listed on the showcase.
NamelessMC - NamelessMC is a free to use and open source website software, built specifically for Minecraft servers who are looking for an all in one, easy to use community hub.
Flarum - Flarum is the next-generation forum software that makes online discussion fun. It's simple, fast, and free.
Invision Community - Invision Community is a flexible, integrated set of apps for building communities on the web.