Flyspray: The Bug Killer! is an uncomplicated, web-based bug tracking system written in PHP for assisting with software development released under the GNU Lesser General Public Licence Version 2.1. Supports MySQL en PostgreSQL backends.
Mantis Bug Tracker is a free popular web-based bugtracking system (feature list). It is written in the PHP scripting language and works with MySQL, MS SQL, and PostgreSQL databases and a webserver. MantisBT has been installed on Windows, Linux, Mac OS, OS/2, and others. Almost any web browser should be able to function as a client. It is released under the terms of the GNU General Public License (GPL).