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.

James Kemp

This plugin allows you to list any number of related posts from the same category as the current post. You can also randomise these results. It is very lightweight, at only 3KB.
There are a number of options available:
<ul>
<li>Choose the number of Posts to show</li>
<li>Choose whether it displays these posts randomly, or in order specified by you.</li>
<li>Choose whether to display a title, what tags to use, and what text should be displayed (e.g. H3)</li>
<li>Choose a class for the main UL</li>
</ul>
To display the random related posts in its simplest form, simply place the following code in your single.php file – <code><?php relatedPosts(); ?></code>.
To edit the options availble, use the following codes:
<pre><code><?php relatedPosts(
 $ppp = 4, 
 $rand = true, 
 $rPinctitle = true, 
 $rPtitletag = 'h3', 
 $rPtitle = 'Related Posts', 
 $rPulclass = 'related_posts',
 $orderby = 'title', 
 $order = 'ASC'
); ?>
</code></pre>
Where:
<ul>
<li>$ppp = Number of posts to display (Any integer allowed)</li>
<li>$rand = sets the display to random (true/false)</li>
<li>$rPinctitle = Displays the title (true/false)</li>
<li>$rPtitletag = The type of tag to wrap the title in (Default h3, but it can be any valid HTML tag)</li>
<li>$rPtitle = The title to be displayed (This can be any text value)</li>
<li>$rPulclass = This sets the class of the ul (This can be any text value)</li>
<li>$rPexcerpt = Displays the post excerpt (true/false)</li>
<li>$orderby = This allows you to order the posts by certain parameters (title/author/date/modified/menu_order/parent/ID/none/comment_count) If you want to choose the order of your posts, be sure to set $rand to false</li>
<li>$order = This can either be Ascending or Descending (ASC/DESC)</li>
</ul>

Random Related Posts Based on Category

This plugin allows you to list any number of related posts from the same category as the current post. You can also randomise these results.

FourNodes Random Post vs Random Related Posts Based on Category