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.

With this plugin you can easily replace the standard WordPress commenting form with one of the popular commenting system’s widget, such as <a href="https://disqus.com/" rel="nofollow ugc">Disqus</a> and <a href="https://www.hypercomments.com/" rel="nofollow ugc">HyperComments</a> or with the VKontakte comments widget.
<h4>Working with plugin</h4>
<ul>
<li>After installation you should go to the plugin settings page in the Comments section and paste the comments widget into a single form field and then click Save Changes.</li>
<li>To get the widget code you will need to register at the appropriate commenting system’s website (or create a simple application for VKontakte).</li>
<li>You can add to the widget code any custom HTML markup.</li>
<li>Any custom text or HTML/JavaScript code will be displayed instead of the standard WordPress comments.</li>
<li>Just leave the field empty to hide the comments on all pages.</li>
</ul>

WP Custom Comments

Replacing the standard WordPress commenting form with custom HTML/JavaScript code.

Disqus Popular Posts vs WP Custom Comments