Allowing users to define their own item types would probably require a large structural change to the application and the database, but here is a suggestion that would provide similar results while working with the functions currently available.
If Administrators could define their own Tabs that were based on one of the existing item types, and with a Filter and a Template defined, they could effectively create their own item types. The new tabs should work exactly like the existing tabs, but with clever use of the Filter and Template it would appear that they displaying a unique item type.
Each project should be individually configured (ie custom tabs should be enabled/disabled for each project).
The Project Setup window could be extended easily. Currently it is possible to select the Template for each of Defects, Features, Tasks & Incidents. New custom tabs should be displayed here also, with an enabled/disabled checkbox and a Filter selectiion. (The standard tabs should also have a enabled/disabled checkbox, but no Filter selection).