Turning on the statistics tweak at Admin -> Settings -> Switches -> "Statistics" will enable a member home area option for members to view statistics and graphs of who's been clicking their links, downloading their files and viewing their articles.
By default, statistics are kept for 30 days. If your site is especially busy you may wish to remove them sooner to keep the database smaller -- you can change the number of days statistics are retained at Admin -> Settings -> General -> "Retain statistics for: ___ days"
Registrations and submissions are also recorded in the statistics table, and you can show these via a toplist if you wish:
Admin Statistics
Note there's also a statistics page in the admin panel. That page shows many of the same things and some different things, but on a global scale instead of for a particular article.
Adding New Statistics
If you want to track another type of click that's not presently tracked, all you need to do is is add id="your_stat_type{LINKID}" class="clicktracking" to the <a> link tag that you want to track-- or leave out the {LINKID} if it's a global stat not associated with a particular article. It'll replace the underscores with spaces in displaying the name of the stat and capitalization will be automatically adjusted to context.