Alternatives to bbPress

Disqus is a Comment-as-a-Service provider that makes it easy to add comments to any web property. It's one of the most popular comment plugins on the market today. With Disqus, publisher can bring their content to life, fuel colorful discussions, efficiently moderate comments, and build engaged communities. The plugin takes only a matter of minutes to setup and is as easy as installing a WordPress plugin or adding a code snippet to your website.

vBulletin is a powerful commercial forum software written in PHP. The software is built to be easily extended through plguins and customized with themes. vBulletin is used to power many of the largest forum, communities and social site across the web. Over 100,000 sites are currenty powered by vBulletin.

A free and open-source modern forum software written in PHP. With Flarum you can eaisly setup your own discussion froum and host it online.

Simple Machines Forum or SMF in short is a free and open-source forum software. SMF can be used to build your own online community that you self-host on a host of your choice. Simple Machines Forum comes packed with features for customization, extension and management of your community. The template engine puts you in control of the design of your community. The plugin architecture makes it easy to extend and provide further feautres though third-party built packages. 

One of the world most popular, free, open-source and self-hosted forum software, written in PHP. With phpBB you can create communities that can be hosted with most hosting providers. The software package is built and designed from the ground up to to be extensible and provides customization option through themes and feature extensions through plugins. The extensive database of user-created extensions and styles database, easy of use, and the simple installation process has made phpBB a common choice among self-hosted forums and communities.

LayerBB is a small yet feature rich, free and open-source community software written in PHP. LayerBB enables you to quickly and easily start your own community while providing great flexibility and customisability.

Create an online community that your customers will love. Vanilla's forum software is used by top brands to engage customers, drive loyalty and reduce support costs. The software is provided free and open-source as a self-hosted solution and can be bought by businesses and enterprises as a managed and hosted solution.

NodeBB is an open source forum software powered by Node.js and supports either Redis, MongoDB, or a PostgreSQL database. With NodeBB you can self-host communities with instant interactions and real-time notifications powered with the help of web sockets. Thousands of organizations have also stared their communites with NodeBB SaaS product, free from self-service and maintinance.

bbPress is forum software from the creators of WordPress. With bbPress you can quickly setup a forum for asyncronous discussion and subscriptions for your WordPress-powered site.

Invision Community is a leading platform for building vibrant communities with forums, eCommerce, content management, image galleries and more. With Invision Community, you can increase your brand or business customer loyalty, reduce support costs and drive sales by building a vibrant online community.

Discourse is an open source internet forum and mailing list software. The application is written with Ember.js and Ruby on Rails, and can be self-hosted in the cloud or on local hardware for free. Discourse also provides managed hosting starting at $100/month, so that you can focus on building a community rather than installing software and managing servers.