Yes, Request Tracker (affectionately known as RT) is just what you're looking for. A support ticket system is exactly what this system was written to do. I originally had it running on a system with Sendmail and have recently moved it to another server that runs Qmail. Both have worked flawlessly. The documentation provided with RT leaves a bit to be desired, but this is basically what you will need in order to build it:
- Apache, built as a DSO preferably
- The RT source (from www.fsck.com)
- HTML::Template perl module
- MySql server
That should get you going. While the documentation is a little sketchy, the e-mail user groups for RT are pretty useful. Go to www.fsck.com for the downloads. If you have difficulty with the install / configure, I would be happy to help. Good luck.