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.

Jonny Harris

Andrew Bartel

DeusMachineLLC

Aaron J White

RenettaRenula

The Disqus Recent Comments Widget plugin will create a configurable widget that will allow you to display comments in any widgetized area of your theme like sidebars and footers.
You can customize the comment length and date format, filter users and choose from three different markup templates, among other things. The plugin has full support for custom markup defined with register_sidebars() and should integrate smoothly with most themes in the wp.org repository.
We try to be very proactive and responsive with support. So, if you have any issues, please post in the support forums and we’ll do our best to resolve your issue promptly.
You can follow development here: https://github.com/andrewbartel/Disqus_Recent_Comments

Disqus Recent Comments Widget

Disqus has dropped support for their recent comments widget.  This plugin creates a configurable widget that will display your latest Disqus comments.

Disqus Popular Posts vs Disqus Recent Comments Widget