The best PHP forum software has got to be vBulletin, because it has unparalleled features and support. The only problem is it costs over a hundred dollars. So that may be a problem if you’re just starting out.
It used to be that the single largest competitor to vBulletin was phpBB, but it’s no longer the case. Recently I discovered a few VERY good free php forum scripts. I’m really amazed by them because all these scripts are lightweight, elegant, and fast! If you are looking to start your own forum, then these are the best free forum scripts that you can find. In no order of preference, they are:
One thing that you MUST consider, however, is the future of your website. These relatively-new forum scripts have a rather different backend structure as compared to vBulletin — and looking through the current database importer scripts that vBulletin provides, only phpBB can be seamlessly imported into vBulletin with ease.
So if you’re looking to upgrade to something like vBulletin, then these forums might not be such a good idea. If you’d like something safer, go with phpBB. It’s free, it’s feature-packed, and it has a huge community that provides support and mods free. In fact, one hugely popular free mod for phpBB is a free WordPress and phpBB bridge plugin.