ProjectPier is a Free, Open-Source, self-hosted PHP application for managing tasks, projects and teams through an intuitive web interface. An opensource version of basecamp! Looks pretty basic, not nearly as ajaxy / designed as 37 signals.
Collabtive is an open source clone of BaseCamp (the 37 signals project management software) built in PHP backed by MySQL.
CRM package from 37Signals, the people behind Basecamp and other Ruby on Railes goodies.