I really like WoltLab, they have a great Forum and the community is generally really nice The customer support is also awesome
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Discourse - Discourse is an open source discussion platform built for the next decade of the Internet.
Crowded Communities - The all-in-one community platform.
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.
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Flarum - Flarum is the next-generation forum software that makes online discussion fun. It's simple, fast, and free.