Four Nodes

Simple plugin to display random posts on your wordpress blog. Plugin provides a widget to display random posts in sidebar. 
Also comes with a shortcode [randomposts] to include on pages.
<ul>
<li>Easy to install</li>
<li>Picks Random Posts</li>
<li>Ability to select from specific category</li>
<li>Limit number of posts</li>
<li>Shortcode support</li>
</ul>

FourNodes Random Post

Displays Random wordpress posts in a sidebar widget. Also, provides shortcode to display random posts on pages.

Brendon Boshell

Stumble! for WordPress extends WordPress to support a “random article” feature, similar to <a href="http://www.stumbleupon.com/stumblethru.php" rel="nofollow ugc">StumbleUpon’s StumbleThru</a> and Wikipedia’s (Mediawiki’s) random article feature.
It has shown that it can significantly increase pageviews on a blog.
The plugin supports basic “go to any random page” functionality, but can also integrate with <a href="http://mitcho.com/code/yarpp/" rel="nofollow ugc">Yet Another Related Posts Plugin</a> to stumble similar articles. Stumble! for WordPress will automatically (optional) give priority to articles with more comments, so users will be brought to your most popular posts.
Since version 0.2, the plugin also shows statistics to show total number of stumbles, and hits to individual articles as a result of Stumble! for WordPress.
New for version 1.0: You can now enter the Stumble! for WordPress network (from the options panel) which will send your traffic from stumbles from other blogs! (and visa-versa)

Stumble! for WordPress

Stumble! for WordPress extends WordPress to support a "random article" feature, similar to StumbleUpon's StumbleThru.

FourNodes Random Post vs Stumble! for WordPress