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.

Aaron D. Campbell

There is a <a href="http://bluedogwebservices.com/problem-related-post-plugins/" rel="nofollow ugc">problem 
with related posts plugins</a>, and Efficient Related Posts is fixing that by 
approaching the problem from a different direction and offering a very different 
solution.
Basically, current related post plugins build the list of related posts on the 
fly when the user needs to view it. Since blogs tend to be viewed far more 
often than they are updated (often hundreds of times more often), these queries 
are run way more times than they need to be. This not only wastes CPU cycles, 
but if the queries are slow (which they will be if you have 1000s of posts and 
tags) then the user gets a poor experience from slow page loads.
Efficient Related Posts moves all this effort into the admin section, finding 
related posts when a post is saved rather than when the user views it. The 
advantage is that if the query is slow it happens less often and the post writer 
is the one that waits rather than the user (which I think is WAY better).
There are limitations. For example, since the related posts are stored as post 
meta data, we only store a certain number of them (10 by default, but you can 
set it to whatever you want). This means that if you decide you need to display 
more than 10, you need to have the plugin re-process all posts. I generally 
display up to 5 related posts, but store 10 just in case I decide to display 
more in some areas. Also, since the related posts are calculated when a post is 
saved, manually adding a tag through the database will have no effect on the 
related posts, although I recommend not doing that anyway.

Efficient Related Posts

A related posts plugin that works quickly even with thousands of posts and tags.  Can be added automatically to the end of posts.

Random Related Posts Based on Category vs Efficient Related Posts