alphasis

The widget area lists posts of the same category as the current post. 
This plugin requires the WP_Widget class introduced in WordPress Version 2.8. 
This widget works when any single Post page is being displayed.
<h4>Official Page</h4>
<ul>
<li>Plugin’s Official Page : <a href="http://alphasis.info/developments/wordpress-plugins/widgets-of-posts-by-same-categories/" title="English" rel="nofollow ugc">English</a> / <a href="http://alphasis.info/2010/11/widgets-of-posts-by-same-categories/" title="Japanese" rel="nofollow ugc">Japanese</a></li>
<li>Author’s Website : <a href="http://alphasis.info/" title="alphasis.info" rel="nofollow ugc">alphasis.info</a></li>
</ul>
<h4>Options</h4>
<ul>
<li>Number of Posts to Show by Categories</li>
<li>Order By
<ul>
<li>Sort by title</li>
<li>Sort by creation date</li>
<li>Sort by last modified date</li>
<li>Sort by numeric post ID</li>
<li>Random</li>
</ul>
</li>
<li>Order
<ul>
<li>Ascending</li>
<li>Descending</li>
</ul>
</li>
<li>Creates a link to each category?
<ul>
<li>Yes</li>
<li>No</li>
</ul>
</li>
<li>Exclude (Categories)
<ul>
<li>The IDs of any categories you want to exclude, separated by commas.</li>
</ul>
</li>
<li>Separator
<ul>
<li>What to separate each category by.</li>
</ul>
</li>
</ul>
<h4>Localization</h4>
<ul>
<li>Japanese (ja) – <a href="http://alphasis.info/" title="alphasis.info" rel="nofollow ugc">alphasis</a> (plugin author)</li>
<li>Current release supports English and Japanese only.</li>
</ul>

Widgets of Posts by Same Categories

The widget area lists posts of the same category as the current post.

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.

Widgets of Posts by Same Categories vs Efficient Related Posts