The Systems Group provides an Issue Tracking service. We run Request Tracker (currently version 3.8).
As a user, every e-mail you send to firstname.lastname@example.org (or other support addresses maintained by the Systems Group) generates a trouble ticket, with a unique number for tracking and resolving the issue.
As a customer, you can request a queue on the RT server. This will provide a web interface for you and your group to track trouble tickets, and an e-mail address users can use to report issues. You can also get reports from the system to track metrics on your tickets.
If you would like to set up a ticket queue, fill out this form.