activeCollab is a free open source project management and collaboration tool. Like a Basecamp open source app, this web-based application is very similar to 37 Signal‘s Basecamp project management tool, but instead of a hosted service, activeCollab is an application you download and install on your web server. The tool requires PHP and MySQL, so should be easy to install on most hosting packages. Aside from the money you’ll save, this appears to be very easy to install and it has most of the functionality of other project management tools.
If it is not too much of it technical or practical inconvenience for you to put it on your own server this will be a preferred solution for many people.