Web Server w/ PHP: If you're not too keen to host your team's projects on a third-party server — or pay the high fees associated with commercial project management tools — Collabtive is an open-source project management suite you self-host.
You'll need a web server to host it on that has PHP on it or if you want to use it on your local Windows machine you can install WAMP. Once you have Collabtive up and running — you can try out their demo before going to the hassle of downloading and installing it — you'll be able to create projects and tasks, assign due dates to them, survey your project progress from the dashboard and calendar, and review project milestones. Because you run Collabtive on your own server it's possible to not only backup data from within Collabtive but backup the entire installation down to the last script — a kind of security you simply don't have when using a tool on 3rd-party servers.
Collabtive is open source and works wherever PHP does. Have a collaborative tool you love? Let's hear about it in the comments.