I created a small test project to check it out. It is a somewhat opinionated software, and may not do some of the things that you expect it to do. For example, by default, there is no option to break down a story into tasks, or to assign points to bugs and technical tasks, but you can change that setting on a per-project basis if you want to. Check out their help section for other things it can or cannot do – Pivotal Tracker help.
And it is free with no limitations! What more can you ask for, go check it out today.

Another good write up on Pivotal Tracker –

Helping web developers and operations bridge the deployment gap
Thoughtworks Mingle vs. Pivotal Labs Tracker.