The Random Featured Post plugin allows you to display a random post from a designated category. Ideally this should 
draw readers landing on your homepage to some of your best posts. The featured post will display the title 
“Featured Post” (customizable) along with the post’s title, an excerpt and a link to continue to the full post.
<h3>Additional Notes</h3>
<ul>
<li>The show_featured_post($PreFeature = ”, $PostFeature = ”, $AlwaysShow = false, $categoryID = 0, $NumberOfPosts = 0) function has five optional arguments. 
The first two are for any HTML you would like to display before and after the featured post. The third argument is a 
boolean (true/false) argument which will override the \’Show Featured Post\’ option and always display the featured post when true. The fourth option allows you to 
specify a single category to display from, overriding the selections in settings page. The fifth option allows you to show more than one post at a time, overriding 
the settings page option.</li>
<li>All output is contained in a DIV class named “featuredpost” and can be adjusted via your stylesheet.</li>
</ul>

Random Featured Post

The Random Featured Post plugin allows you to display a random post from a designated category as a "featured" post.

cleancodenz

If your wordpress site is tracked by Google Analytics, then you can get access to all those stats about your site like visitors, keywords and pageviews. But it is not easy to present some of those stats on your wordpress site if you want to, like which posts are visitor’s favorite posts? because data in Google Analytics 
about the sites you are tracking are private to the account holder, not to the general public.
This plugin uses Google Analytics API to get the stats of favorite posts of your wordpress blogs and list them in a table
To use this plugin, you need a Google Analytics Account and a profile which is your wordpress install, your Google Analytics information are encrypted and saved in options.
Any issues: <a href="http://www.cleancode.co.nz/contact" rel="nofollow ugc">contact me</a>.

CleanCodeNZ Favorite Posts Plugin

This plugin uses Google Analytics API to get the stats of favorite posts of your wordpress blogs and list them in a table

Random Featured Post vs CleanCodeNZ Favorite Posts Plugin