Collabtive is a free PHP project management software with a Web 2.0 looking, ajaxed interface.
The software is still in the beta phase but it already has the features like:
- Projects, Milestones, Taskslists, Tasks
- User management
- Message system
- Integrated instant messenger
- Multilingual
- Template system

Activecollab was one of the most popular free project management softwares that became a paid solution after sometime. If you are looking for an alternative which will run on your servers & have an open source code, take a look at Collabtive.
There are some nice upcoming features like a flash progress meter for the projects.
Requirements: PHP, MySQL
Redmine is a flexible project management web application. Written using Ruby on Rails framework, it is cross-platform and cross-database.
With a plain interface which makes the use easier, Redmine has most of the features a project managemnt software must have like multiple projects, role based access control, wiki & file management.

Redmine features:
- Multiple projects support
- Flexible role based access control.
- Flexible issue tracking system
- Gantt chart and calendar
- News, documents & files management
- Feeds & email notifications.
- Per project wiki
- Per project forums
- Simple time tracking functionality
- Custom fields for issues, projects and users
- SCM integration (SVN, CVS, Mercurial, Bazaar and Darcs)
- Multiple LDAP authentication support
- User self-registration support
- Multilanguage support
- Multiple databases support
Redmine is in beta status yet and improved regulary.