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.
easy TicketManager is a system for managing customer requests (trouble tickets or similar) for a group of users. Each ticket is assigned to a customer and a carer who is responsible for handling this ticket. Tickets can be organized in folders or by categories and can have notes attached to them.