wkrzysztofik

This plugin allow to use new widget – Most liked posts. This widget displays list of posts ordered by number of Facebook likes. Number of likes is updated hourly by wp cronjobs. Plugin doesn’t require any additional configuration. Just install, add widget to your sidebar area and have fun!

Most Liked Posts

Wordpress widget displaying list of posts ordered by number of Facebook likes.

Nader

The “Most Comments” plugin displays as the name says posts with the most comments. You can either use the widget in the sidebar or integrate the plugin as template tag in your theme files.
Features:
<ul>
<li>Limit the amount of posts to be shown</li>
<li>Show comments from a specific post category</li>
<li>Exlude posts without comments</li>
<li>Select a time range (last XX days) of posts to be taken into account</li>
<li>Customize the design template via the settings page</li>
<li>Place a widget in your sidebar</li>
</ul>
More Information & Feature Description: 
http://www.brandinfection.com/wordpress-plugins/most-comments/
<h3>Configuration</h3>
You can configure the most comments plugin to your needs. Options can be found under the menu <code>Settings > Most Comments</code>

Most Comments

Display posts with the most comments, as a widget or on a page using the template tag. Customize the look with specific settings.

Most Liked Posts vs Most Comments