Can I track the click of every link, button, dropdown select, etc. on a screen and have it be tracked in Google Analytics?

I want to create a page and collect data on which widget the users use most.

What about AJAX stuff? What if you're using jQuery or Mootools...can you get the functions to register a fake URL with GA based on user interaction? I use to do this with Flash. Everytime you click a button, it can initiate a fake URL request. I would make urls such as ".../customize/eyes/" or ".../customize/nose", etc. Just wondering if I can do that with Javascript on the page.

I've also posted at StackOverflow.