Scott Reilly

This plugin adds a checkbox to the profile page for users which allows them to opt into receiving a notification email whenever a comment is made to the site.
If a comment goes into moderation, only users who have the ability to manage comments on the site will receive the moderation notification email.
By default, all users of the site have the ability to subscribe to notifications about comments. A filter is provided to facilitate use of code to customize the feature’s availability to users.
Note: a “user” is a person with an actual login account for the site. The plugin does not facilitate permitting visitors who do not have an account on the site to be able to subscribe to all comments.
Links: <a href="http://coffee2code.com/wp-plugins/optin-comment-notifications/" rel="nofollow ugc">Plugin Homepage</a> | <a href="https://wordpress.org/plugins/optin-comment-notifications/" rel="ugc">Plugin Directory Page</a> | <a href="https://github.com/coffee2code/optin-comment-notifications/" rel="nofollow ugc">GitHub</a> | <a href="http://coffee2code.com" rel="nofollow ugc">Author Homepage</a>

Optin Comment Notifications

Checkboxes on user profiles to receive emails about new comments. Like it says.

Exactly what you want

Allows users to opt into receiving a notification email whenever a comment is made to the site.

Daniel Bachhuber

Easily subscribe to a P2 comment thread without commenting using a “Follow” action link like WordPress.com has.
This plugin requires Jetpack and P2 to both be activated. It doesn’t yet allow you to unfollow, and there are some minor interface quirks.
Happy to receive feedback, questions, feature suggestions, and <a href="https://github.com/danielbachhuber/Jetpack-Follow-Link-for-P2" rel="nofollow ugc">pull requests</a>

Jetpack Follow Link for P2

Easily subscribe to a P2 comment thread without commenting using a "Follow" action link like WordPress.com has

Optin Comment Notifications vs Jetpack Follow Link for P2