ProjectPier is a Free, Open-Source, PHP application for managing tasks, projects and teams through an intuitive web interface. It must be downloaded and installed on your own web server. ProjectPier will help your organization communicate, collaborate and get things done Its function is similar to commercial groupware/project management products, but allows the freedom and scalability of self-hosting. Even better, it will always be free.

Project management software recommended by Marty Kearns on ProgX.

GTD Software Online for Getting Things Done

Ticketish is a simple web-based system for managing help tickets. With an emphasis on more benefit, and less mess, Ticketish is perfect for small to medium-sized teams who need something that will get the job done and get out of the way.

Bug Tracking, Issue Tracking, & Project Management