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.

xdark

Easy Related Posts is a WordPress plugin that displays posts related to the one a user is currently reading. 
Easy Related Posts can display related posts in main content area or in sidebars through a widget. 
Equipped with 3 eye catching fully responsive themes, supports basic modifications on them from admin panel. It also has a theme system that let you modify or write your own themes to match you personal needs. 
Through an intuitive algorithm it creates “relations” between posts and rates them based on posts categories and/or tags in a way so these ratings are as much as accurate they can be. 
Last but not least in any way, Easy Related Posts uses the best coding standards and practices with mind in security.
If you like this plugin please support the developers. You can do so using the links inside plugin settings page or by purchasing the PRO version.
PRO version can be purchased from <a href="http://erp.xdark.eu/downloads/easy-related-posts-pro/" rel="nofollow ugc">here</a>. 
To see a full list of features and compare them to the PRO version please visit <a href="http://erp.xdark.eu/version-comparison/" rel="nofollow ugc">this page</a>.
Easy Related Posts wont spam your visitors with content from other sites, ads or in any other way.
<a href="http://erp.xdark.eu/demo/" rel="nofollow ugc">See the demo</a>
This plugin requires PHP version 5.3 and above.
Features:
<ul>
<li>Easy to setup</li>
<li>Choose displayed content: excerpt length, thumbnail resizing and many more.</li>
<li>Choose if related posts should be fetched by categories or by tags</li>
<li>Exclude posts that have certain categories and/or tags from related posts</li>
<li>Prevent related posts from spawning in certain categories or tags</li>
<li>Display related posts as an eye-catching pop up block</li>
<li>Display related posts through a widget or/and in main content area</li>
<li>Options optimized before activation for most of the cases</li>
<li>Really fast, not a single database entry (I really love clean DB’s)</li>
<li>Responsive design</li>
</ul>
Please report any bugs or features you’d like to see in feature releases <a href="http://erp.xdark.eu/bugs/set_project.php?project_id=3" rel="nofollow ugc">here</a>

Easy Related Posts

Displays related posts in the end of each post or/and in sidebar through a widget

Widgets of Posts by Same Categories vs Easy Related Posts