Google Analytics provides a sophisticated visitor-click tracking system based on Urchin. You can track visitor clicks on any object of the webpage including Javascript, Flash elements, Banners, Graphics and even downloadable files like PDF.

Here's a quick primer on enabling tracking mechanism in Google Analytics. [source: Google Analytics Help]

Track clicks on links that lead to file downloads (such as PDF, AVI, or WMV)

You'll need to tag the link itself with the urchinTracker JavaScript if you would like to track these downloads. This piece of JavaScript assigns a pageview to any click on a link. For example, to log every click on a particular link to www.example.com/files/map.pdf as a pageview for /downloads/map you would add the following attribute to the link's <a> tag:

<a href="http://www.example.com/files/map.pdf" onClick="javascript:urchinTracker ('/downloads/map'); ">

Track which advertisers are popular by tracking clicks on banners ads where visitors click on to leave your site.

To track outbound clicks on an animated GIF or other type of static banner ad, add the following code within the <a> tag (You may use any folder/filename structure that you desire)

<a href="http://www.advertisersite.com" onClick="javascript:urchinTracker('/bannerads/advertisername/bannername');">

The equivalent code for a Flash banner is provided below:
on(release) {
getURL("javascript:urchinTracker('/bannerads/adname/bannername');");
getURL("http://www.advertisersite.com");
}

Track clicks on outbound links that lead visitors away from your site.

You will need to tag the link itself with the urchinTracker JavaScript. For example, to log every click on a particular link to www.example.com as a pageview for "/outgoing/example_com" you would add the following attribute to the link's <a> tag:

<a href="http://www.example.com" onClick="javascript:urchinTracker ('/outgoing/example_com');">

Track JavaScript events like RollOver or OnMouseOver

To track an event, use the urchinTracker JavaScript function to specify a name for the event. The following illustrates how to log an onClick event:
<a href="javascript:void(0);" onClick="javascript:urchinTracker('/folder/file');">

Or, to log a rollover event:
<a href="javascript:void(0);" onMouseOver="javascript:urchinTracker('/folder/file');">

Related Reading:

10 Things about Google Analytics you may not know
Screenshots of Google Analytics system
The circle of analytics