Rolf Allard van Hagen

This plugin could also have been called Don’t bother the Site Administrator with every other author’s Comment Moderation Notifications, unless the author has no moderation rights but since that’s a slightly longer title, I chose to keep it as simple as I could. However, it explains well what this plugin does:
Normaly, when a comment gets submitted to a particular post, the author of that post gets a notification about it. But when that comment is held for moderation (which depends on your sites comment settings) then the moderation notification is sent to both the post Author (if he/she has moderation rights) and the sites Administrative moderator e-mail address as configured under Settings > General at the same time.
For many blogs or sites where the owner is the only author and his/her account uses the same e-mail address as the Administrative moderator e-mail address, this will boil down to one message to one address. But when the Site Admin is not the only author, like on colaboration sites or sites managed by a webmaster or designer where other people like the client usually posts, this might result in flooding the admins mailbox with moderation messages that are not really his/her concern. The site admin, with enough on his/her mind already, is bothered with each and every new comment in the moderation queue.
This plugin changes that.
Just install and activate it: All post comment moderation notifications will be sent only to each respective Post Author. If, by any chance, the post author has no moderation rights (Contributor level) or there is no author e-mail set then the default site e-mail address will still get the notification.
WordPress Multisite compatible, per-site or network activated or as a must-use plugin.

Comment Moderation E-mail only to Author

Works great

Still works !

Send comment moderation notifications ONLY to the Author, not to the site Administration address any more.

Yasir

UPDATE: Users now have three options to choose from:
<ol>
<li>
Do Not Send Email Notifications.
</li>
<li>
Send Email Notification ONLY If Someone Replies To My Comment(s).
</li>
<li>
Send Email Notification Whenever A New Comment Is Posted.
</li>
</ol>
If a user chooses the second option, then email notification will only be sent to him when someone reply to his/her comment by clicking on Reply button below the comment.
You can find more information here: http://elance360.com/wordpress-plugin/
For this plugin to work, you will need to enable Threaded/Nested comments option.
:Send email only on Reply to My Comment: is a Modified version of this plugin :Subscribe To Comments Reloaded:
<h3>Requirements</h3>
<ul>
<li>WordPress 2.9.2 or higher</li>
<li>PHP 5.1 or higher</li>
<li>MySQL 5.x or higher</li>
<li>Threaded/Nested comments option Enabled</li>
</ul>
<h3>Main Features</h3>
<ul>
<li>Simple to use</li>
<li>For the second option, email will only be sent if a person chooses to get notification and if the new commenter has pressed the Reply Button on his comment.</li>
</ul>
<h3>Language Localization</h3>
:Send email only on Reply to My Comment: is a Modified version of :Subscribe To Comments Reloaded: I have modified this plugin so that email notifications are NOT sent to all subscribers, instead only one notification is sent to the Original Poster :if he has selected to receive notifications:.
:Subscribe To Comments Reloaded: supports different languages. There is a langs directory containing .mo and .po files. If you want to use another language, then you will need to search and find how plugin language can be changed. I cannot provide any support in this regard. 
Supported languages.
<ul>
<li>Danish</li>
<li>Dutch</li>
<li>French</li>
<li>German</li>
<li>Indonesian</li>
<li>Italian</li>
<li>Norwegian</li>
<li>Polish</li>
<li>Portuguese, Brazil</li>
<li>Portuguese, Portugal</li>
<li>Russian</li>
<li>Serbian</li>
<li>Spanish</li>
<li>Turkish</li>
</ul>

Send email only on Reply to My Comment

UPDATE: Users now have three options to choose from:

Comment Moderation E-mail only to Author vs Send email only on Reply to My Comment