While it is not web based, I use Microsoft Outlook in a networked environment and customise the "Task" items.
Creating the database is as easy or easier than Access, but Outlook manages all the little frills for you, due dates, email notification, status, reporting, the assigned to person, etc. There are a few books around on developing applications in Outlook and even the MS Press one is good.
Actually the MS Press one has a sample Helpdesk application on the included CD which is very close to what you want.