Bugzilla is most popular and widely used "Defect Tracking System" or "Bug-Tracking System". Defect Tracking Systems allow individual or groups of developers to keep track of outstanding bugs in their product effectively. Most commercial defect-tracking software vendors charge enormous licensing fees. Despite being "free", Bugzilla has many features its expensive counterparts lack. 
	Bugzilla is used to 
	<ul>
	<li>Track bugs and code changes</li> 
	<li>Communicate with teammates</li> 
	<li>Submit and review patches</li> 
	<li>Manage quality assurance (QA)</li>
	</ul>
	 Its feature includes: 
	<ul>
	 <li>Advanced Search Capabilities</li>
	 <li>Email Notifications Controlled By User Preferences</li>
	 <li>Bug Lists in Multiple Formats (Atom, iCal, etc.)</li>
	 <li>Scheduled Reports (Daily, Weekly, Hourly, etc.)by Email</li>
	 <li>Reports and Charts</li>
	 <li>File/Modify Bugs By Email</li>
	 <li>Time Tracking</li>
	 <li>Request System</li>
	 <li>Private Attachments and Comments</li> 
	 <li>Automatic Username Completion or Drop-Down User Lists</li>
	 <li>Patch Viewer</li>
	 <li>"Watch" Other Users</li>
	 <li>Move Bugs Between Installs</li>
	 <li>Save and Share Searches</li>
	 <li>Excellent Security</li>
	 <li>Powerful Extension Mechanism for Highly Customizable Installations</li>
	 <li>Custom Fields</li>
	 <li>Custom Workflow</li>
	 <li>Full Unicode Support</li>
	 <li>Localization</li>
	 <li>mod_perl Support for Excellent Performance</li>
	 <li>Webservices (XML-RPC) Interface</li>
	 <li>Control Bug Visibility/Editing with Groups</li>
	 <li>Impersonate Users</li>
	 <li>Multiple Authentication Methods</li>
	 <li>Support for Multiple Database Engines</li>
	 <li>Sanity Check</li>
</ul>

Bugzilla is most popular and widely used "Defect Tracking System" or "Bug-Tracking System".

Bugzilla

Phabricator is an open source collection of web applications which make it easier to write, review, and share source code. It has Wiki and CLI support. Phabricator was developed at Facebook. 

Phabricator - Continuous Release Management from Facebook

Eventum is a user-friendly and flexible issue tracking system that can be used by a support department to track incoming technical support requests, or by a software development team to quickly organize tasks and bugs. 

Eventum - issue tracking system

It does everything from bug tracking and customer support to project management and to-do lists. It is light weight and web based as it is written in CGI. It has support for Ticket monitoring, Custom fields, Inventory Tracking, Custom fields, Email alerts, File attachments etc. 

 It has reporting and search functionality. It does have backup and restore functionality to migrate the data. 

 Demo: <A HREF="http://www.troubleticketexpress.com/trouble-ticket-demo.html" target="_blank">http://www.troubleticketexpress.com/trouble-ticket-demo.html</A>

It does everything from bug tracking and customer support to project management and to-do lists. It is light weight and web based as it is written in CGI. It has support for Ticket monitoring, Custom fields, Inventory Tracking, Custom fields, Email alerts, File attachments etc.

Trouble ticket express - Help desk software in Perl and CGI

Request Tracker (RT) is an enterprise-grade issue tracking system which thousands of organizations use for bug tracking, help desk ticketing, customer service, workflow processes, change management etc. This product is very stable and been around for over 10 years. 

 It has loads of features like Dashboard support, Seamless PGP support for mails, Richtext editing, Time tracking etc. It has support of more than 15 languages. RT provides a REST API and even a command-line client to talk to RT from other programs and integrate with other systems.

Request Tracker is an enterprise-grade issue tracking system which thousands of organizations use for bug tracking, help desk ticketing, customer service, workflow processes, change management etc. This product is very stable and been around for over 10 years.

Request Tracker - issue tracking system in CGI and Perl

MantisBT is a web-based bug tracking system written in the PHP and works with MySQL, MS SQL, and PostgreSQL databases and a webserver. It supports multiple projects in a single instance. Its features set include Full text search, Built in Reports, Custom fields, Change History, RSS Feeds, Export to csv, Excel, Word, Upload attachments, Wiki Integration ,LDAP Integration, SOAP interface, Support for mobile devices, localization support and lot more.

MantisBT - Bug Tracking System in PHP

Flyspray is a lightweight, web-based bug tracking system written in PHP for assisting with software development and project managements. It supports Multiple projects, File attachments, Advanced search features, Atom/RSS feeds, Voting for tasks, Comments, Roadmaps and lot more.

Flyspray - Web-based Bug Tracking System in PHP

JTrac has all the features that you would expect from a standard issue-tracking application such as support for file-attachments and e-mail integration. JTrac offers powerful customization options, especially in the areas of workflow and field-level permissions and compares well to even commercial tools. 
 Its feature include: 
 <ul><li>Extremely easy to install</li><li>Unlimited project spaces per installation</li><li>Custom fields and drop-downs for each project</li><li>Customizable workflow per project</li><li>Field-level permissions</li><li>Detailed history view</li><li>E-mail notifications</li><li>File attachments</li><li>Full text search</li><li>Filter searches even by custom fields </li><li>Detailed dashboard view of statistics</li><li>Export data and search results to Excel</li><li>Support for anonymous browsing of projects </li><li>Cross-reference items to each other, e.g. 'duplicate of', 'depends on' etc. </li><li>Translated into multiple languages (Spanish, French, German, Russian, Japanese, Chinese and more)</li><li>Platform independent and various databases supported</li><li>Support for LDAP, Active Directory or CAS based authentication </li><li>Embedded database and web-app server - download and start using right away!</li></ul>

JTrac is an open source and highly customizable issue-tracking web-application written in Java.

JTrac

Squash is an exception reporting and bug analysis tool from Square. Squash lets you analyze information about a bug to determine its root cause. Squash includes a full-featured commenting system, ticket-management system. Squash analyzes the stack trace of every exception, and determines which line in the backtrace is the source of the bug. It then uses git to figure out who might have caused the bug, 

Squash - Bug Smashing Tool

Singlebugs is a sole developer focused bug tracking tool. It takes its interface interface cues from Outlook's three panel design where the leftmost are the projects, the middle the issues and the right running commentary. It has a fulltext search bar which searches across all three streams making a very fluid development experience. Since it is designed to work locally it is also very fast.

SingleBugs -  A simple single person bug tracker

The open source ticket/issue tracker that can track anything. It supports multiple projects and each project could have flexible fields, categories, status and status workflows. Data could be exported as CSV. Each User can customize their own dashboard. Demo: <A HREF="http://demo.elastik.jarofgreen.co.uk/mod.DemoSignUp/" target="_blank">http://demo.elastik.jarofgreen.co.uk/mod.DemoSignUp/</A>

The open source ticket/issue tracker that can track anything. It supports multiple projects and each project could have flexible fields, categories, status and status workflows. Data could be exported as CSV. Each User can customize their own dashboard.

Elastik - issue tracker that can track anything 

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