Bugzilla is the leading open-source/free software bug tracking system, with high-profile installations at mozilla.org, GNOME, Red Hat, and NASA, among others. It features a comprehensive set of fields, attachment management, inter-bug dependencies, email notification of changes, a powerful query interface, reporting, and Web, XML, email, and console interfaces. It can be managed entirely using a Web-based UI. The user UI is customizable using templates.
GNA Frontdesk is a groupware application designed for customer support and bug tracking. People e-mail their messages into a threaded central repository which may be accessed via the web. The Frontdesk groupware system is written entirely in Perl and currently runs under any platform that supports perl.
GNATS is a portable incident/bug report/help request-tracking system which runs on UNIX-like operating systems. It easily handles thousands of problem reports, has been in wide use since the early 90s, and can do most of its operations over e-mail. Several front end interfaces exist, including command line, emacs, and Tcl/Tk interfaces. There are also a number of Web (CGI) interfaces written in scripting languages like Perl and Python.
RT is an industrial-grade trouble ticketing system. It lets a group of people intelligently and efficiently manage requests submitted by a community of users. RT is used by systems administrators, customer support staffs, NOCs, developers, and even marketing departments to track issues, outages, bugs, requests, and all kinds of other things at thousands of sites around the world.