Ashish Kumar (Ashfame)

Plugin offers a admin screen to select the posts of which commentators should be emailed, and then you can write the subject & message to send and the plugin will send them an email along with their comment history on the selected posts.
You also have the option of excluding list of emails and specifying a Bcc email address.
If you find a bug, please report the issue here – https://github.com/ashfame/email-posts-commentators/issues

Email Posts Commentators

Jordi Cabot

In the Settings->Discussion page, authors of a post can use the checkbox Email me whenever – Anyone posts a comment.
But this does not send an email as well to the site admins. In blogs where you have a number of guest authors, you may want to be informed about all the new comments so you can respond (if the author is missing) or just participate in the discussion.
As a site admin myself, I was missing many comments. This means plenty of missing opportunities to engage with your audience.
To solve this situation, the plugin adds a new checkbox in the Discussion page. If checked, admins will get an alert email for new comments.

Comment Admin Notifier

Very simple plugin that doesn't try to do many things. But the one it does is very useful: as a website owner you want to make sure you're on top of all the comments in the site even comments to posts you didn't write. 

It does one thing and it does it right

With this plugin, admin users get an email alert every time a new comment is posted on ANY post in the site.

Email Posts Commentators vs Comment Admin Notifier