1. Bugzilla is by far the most famous, though it is notoriously difficult to set up. Many different companies and Open Source projects use this as their bug tracker.
http://www.bugzilla.org/

2. Mantis: This one is much easier to set up than Bugzilla, and has some pretty limited requirements. I’m not very fond of the UI, but it’s a capable program.
http://www.mantisbt.org/

3. My favorite open source bug tracker is Flyspray. It is simple to install and has a good number of features without being too complicated. I would recommend this one, though you should also take a look at Mantis to see which UI works better for you.
http://flyspray.org/

4. One of the lesser known open source tracker is Eventum. This was made by the developers of MySQL, and has time tracking features unavailable in Flyspray and Mantis. I found it to have far more features than I needed, but depending on what your requirements are, it may be the best fit.
http://eventum.mysql.org/

Alternatively you could find a CMS with a bug tracking addon, such as Drupal (and the project module), or TikiWiki (and their Tracker addon).
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