The once to be board software for Ylilauta. Might not always be open source.
Ultimate PHP Board is completely text based making it easy for anybody who has access to PHP can run a messageboard of their own without the need for MySQL.
Luna is an easy and beautiful solution to build your own board.
Board software in PHP using MySQL. Based off ABXD.
Kanban project management software
A simple task board to help managing software projects.