Mark Jaquith

This plugin notifies people when the comment they just left is moderated or marked as spam. The method of notification can be either a Javascript popup, or an HTML notification in the comment area. You can choose whether spam comments, moderated comments, or both will result in the notification. This is especially useful for spam comments, as the human author will know to contact you and have you rescue the comment from the spam bin.

Antispam Collateral Condolences

Notifies people when their comment is moderated or caught as spam, so they aren't left wondering.

3D Virge

With this plugin you can switch the different WordPress notification e-mails on and off, like options as the new user and password change notifications send by WordPress to the administrator and user. Works perfectly in combination with a lot of other plugins!
Watch this nice tut made by Robert Orzanna: 
<iframe loading="lazy" class="youtube-player" width="750" height="422" src="https://www.youtube.com/embed/66UkQKgSFio?version=3&rel=1&showsearch=0&showinfo=1&iv_load_policy=1&fs=1&hl=en-US&autohide=2&wmode=transparent" allowfullscreen="true" style="border:0;" sandbox="allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox"></iframe>
The options you can manage are:
<ol>
<li>New user notification to admin</li>
<li>New user notification to user</li>
<li>Notify post author</li>
<li>Notify moderator</li>
<li>Password change notification to admin</li>
<li>Password change notification to user</li>
<li>E-mail address change notification to user</li>
<li>Forgotten password e-mail to user</li>
<li>Forgotten password e-mail to administrator</li>
<li>Automatic WordPress core update e-mail</li>
<li>Automatic WordPress plugin update e-mail</li>
<li>Automatic WordPress theme update e-mail</li>
<li>Send admin notifications to extra admin e-mail addresses (1.7.0)</li>
<li>Send an e-mail to administrators after a user requested to update his or her e-mail address (1.7.0)</li>
<li>Send an e-mail to administrators after a user successfully updated his or her e-mail address (1.7.0)</li>
<li>Multi-site support! Now you can manage your notification settings in one single environment (1.8.0)</li>
<li>Export and import settings (1.8.0)</li>
</ol>
The automatic core, plugin, and theme updates have a special built-in feature. When one of these options is disabled, successful e-mails don’t get send out, but failed updates still will send an e-mail to the admin.
This version contains some nice new stuff. If you find any issues, let me know. If you like the new features, please be so kind to give this plugin a good rating! It will help me to keep up the good work for you 🙂
Want regular updates? Feel free to support me with a small donation 🙂

Manage Notification E-mails

Enable and disable email notifications that WordPress sends to the admin and user. Works perfectly with many other plugins!

Antispam Collateral Condolences vs Manage Notification E-mails