I've seen the following:

• One handler which dispatches to a bunch of subs in the handler to handle each request. Some shared data in the handler's package globals, mostly transient data which is either written out to a DB or discarded at the end of a transaction.
• A plugin-like organization, where the URL path is cleaned up and rewritten into a class name; main handler looks to see f the class is loaded and calls a specific method (run(), go() etc.) to execute the request.

Earlier versions actually generated HTML inline (whee! it's 1990 again!); more current stuff uses a templating system to move off the HTML generation into a separate concern.

Tangent: Most of the MVC frameworks are inheritance-based, which means you have to understand a lot about what you're subclassing to do that successfully. The Cocoa and Cocoa Touch frameworks get round this by using delegation for most of the application customization; the base framework does almost all of the basic work, while you just write customization code to do your specific stuff. As far as I know there's no OSS equivalent (maybe GNUStep, but that's not a Perl Web framework). If you want to make a name for yourself, there's a big opportunity!