Cruciforum: crucially simple: Apparently the most simple discussion forum in the world. There’s exactly one file.
Cruciforum is a very simple web forum, designed to make it really easy to add a discussion forum to a website. If you want to start off some conversation around a bit of code you’ve written, provide somewhere to let people enter feature requests, or just want somewhere to chat with your mates, Cruciforum is for you.
You make a folder and drop the single PHP script in it. Data storage consists of the script writing out HTML files around itself. If you want user accounts, look elsewhere.
Limited use, but I appreciate the simplicity of it. For a small step up in complexity, consider bbPress. For the next step up, try Vanilla. On the other end of the extreme, Invision Powerboard is about the ultimate in this space.