scribu

Scenario
You’re the only user who can create posts and moderate comments on your WordPress installation.
You have both ‘Email me when anyone posts a comment’ and ‘Email me when a comment is held for moderation’ options checked.
You get an email about a comment awaiting moderation and you approve it.
The problem is that right after that you get a second email letting you know that a new comment has been posted, which of course you already knew about.
Solution
Instead of disabling email notifications for new comments alltogether, you can use this plugin and not receive the redundant emails mentioned above.
Links: <a href="http://scribu.net/wordpress/filter-email-notifications" rel="nofollow ugc">Plugin News</a> | <a href="http://scribu.net" rel="nofollow ugc">Author’s Site</a>

Filter Email Notifications

Stop WordPress from sending email notifications for comments that have been manually approved.

Eleas Kanchon

Simple Notify is a customizable notification system that enables you to send notifications to both admins and users. The notifications can be delivered via email and can also be displayed directly in the dashboard for easy access.
Key Features: 
– Welcome Email when new user register 
– New Post Publish Email 
– Customizable notification settings 
– Customizable Email Template

Simple Notify

Simple Notify is a customizable notification system that allows you to send notifications via email.

Filter Email Notifications vs Simple Notify