One of the reason why people use Stumbleupon is because it is easy. People click on the Stumble button, and it opens a new page, that they either like, or they click the stumble button again to go to the next site. In WordPress, you can setup a stumbleupon like browsing system where your user can click on a button which will open a random post from your site.
Once you install this plugin, all you have to do is create a graphic button that says Random and link it to:
You can display it as a link also.
With this simple plugin in place, you can significantly increase your pageviews and potentially get more user interaction.
Edit: The Demo link was removed because it puts a lot of load on larger databases.