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.

piffpaffpuff

Related Links gives you the possibility to manually link other posts to your current post. But you can also link pages, media or any custom post-type. And in addition you can use custom urls to link to external files. The plugin adds a Metabox to the writing page with a list of all available content.
Features:
<ul>
<li>Shows a list of all available content in a Metabox on the writing page</li>
<li>Multiple links can be selected</li>
<li>Link order can be changed through drag and drop</li>
<li>Custom URLs can be added</li>
<li>Search field to quickly find a link</li>
<li>Simple theme integration with an included widget or <code>related_links()</code></li>
<li>Works with custom post-types</li>
<li>Settings to enable the post-types that should be shown in the Metabox</li>
</ul>

Random Related Posts Based on Category vs Related Links