This plugin adds a new widget which can show statistics for your blog’s/forum’s 
Disqus comments: most popular discussions, top commenters, recent comments.
Configurable are: 
 * Color Theme 
 * Number of items to show 
 * Default tab view (most popular discussions, top commenters, recent comments) 
 * Whether to show the standard WordPress widget title bar 
 * Title of the widget in the title bar

Disqus Widget

Allows the user to display statistics for their blog's/forum's Disqus comments.

godthor

This will create a new widget which will display your most popular posts and pages based on comment count with Disqus. Alternatively, you can use a shortcode as well.
It’s very simple to use. Just drag the widget into a sidebar and configure it, or visit the settings under the WordPress Settings menu.
Just Some of the Options:
<ul>
<li>Show featured image.</li>
<li>Choose featured image size.</li>
<li>Choose featured image alignment.</li>
<li>Show the post date.</li>
<li>Select how many days to check, IE: past 90 days.</li>
<li>Set how many posts to show.</li>
<li>Save the results for faster loading.</li>
<li>Load results using Ajax. Perfect to avoid caching results.</li>
</ul>
Note: This plugin requires you have an application registered with Disqus: https://disqus.com/api/applications/ 
It’s free and simple to setup, just follow that link.

Disqus Popular Posts

Creates a widget to show the most popular posts and pages on your site based on Disqus comments. Can also be used with a shortcode.

Disqus Widget vs Disqus Popular Posts