I know of osTicket, are there any other more compelling help ticket systems?
My company wants to use one and I am researching them now.
I forgot to mention, I will need to install it on our servers...so SaaS (software as a service) doesn't work.
There is good information on Wikipedia at
Personally, I'm fond of Trac, which has the capability of integrating with subversion, so when you check in a file, if you say something like...
$ svn ci -m "automatically fix any broken dates in the input. fixes #87"
....then Trac will automatically add this comment and close bug #87 for you.