Ofortuna is a mediawiki extension that allows you to display a random page from a specified category.
It works like the Special:Random feature of mediawiki, but whereas in Special:Random you type Special:Random/Wikipedia to see a random page from a namespace, in ofortuna you type Special:ofortuna/Countries to see a random page from a category.
It is available under a free licence. It has no warranty. The current version is preliminary, so expect some time after you can see all of its beauty.
You may find it at http://nsk.karastathis.org/index.php/Ofortuna