Forums are particularly popular on the Internet, since unlike blogs, they allow discussions to be created on various topics. Which is the best forum software?
Most of the new users, when they want a free forum software, their mind goes to phpBB which is very popular. The fact that it is popular does not mean that it is the best, since it is always has problems with its safety. The good thing is that there are several better (and safer) options than phpBB.
Simple Machines Forum
SMF is a pretty good and popular forum system. It has a large and active community, which means support and many options on themes and extensions (plugins). Its good is that it's pretty simple to use and safe, while its minus is that installing the plugins requires to edit its php files, so if someone tries to install a lot can get confused sometimes or even worse, if you want to upgrade the forum, you will lose the plugins.
MyBB is one of the best free forums, and some compare it with some commercials forum software (and they are right). Especially the latest version of MyBB (1.8), makes it particularly attractive. Its good is that its plugins are integrated into the system without the need to edit a file, just like the Wordpress.
esoTalk is a modern piece of software, with a touch that we do not often see on forums. This is a new software, so there are not many extensions and themes yet.
ElkArte is the new fork from some SMF's old developers. Generally there is a trend from developers/participants to leave a platform and make their own. ElkArte is based on SMF and its code is almost the same (though, as with FluxBB, it will change gradually). An important difference, however, is their themes, which fully supporting mobile devices.
FluxBB (a fork of PunBB) is an alternative option to create a forum. Is light enough and very fast, since it does not have many features out of the box, like the above options.
ModernBB is a similar software to FluxBB, as it is based on that. It's a relatively new software and there are certainly not many themes and extensions for it.