We have used JIRA and Alexsys Team for ticketing and happy with both products have their strengths and weaknesses and use them for internal vs. external projects. Had we know about JIRA though in the beginning I personally would have voted for JIRA now using them both for years.
I love the customizability of both, and they both have web interfaces. JIRA's web interface and far superior than Team's but Team has solid custom fields.
JIRA supports multi-level and grouping of issues, Team does not.
JIRA requires work for good reports, reports are easy on Team's database. JIRA though has built in dashboards and you can build more.
JIRA allows people to respond to tickets via email and it automatically get add to the ticket as well as add watchers.
JIRA can be built upon with free and commercial add-ons as well as extended integration with other products. Alexsys can be extended, but has some catches and limitations.