Mark Jaquith

Comment management in WordPress isn’t too hard when you manually approve each comment. You know which comments you’ve seen, and which you haven’t. The only downside is that you have to approve the comments before they appear. Comment Inbox gives you the ease of the moderation queue with the freedom of unmoderated comments. It’s a better way to deal with spam and bacn on your blog.
Here’s how it works:
<ul>
<li>All comments except caught spam go into moderation (renamed “Comment Inbox”)</li>
<li>All comments in your Comment Inbox immediately show up on the blog — so conversations don’t wait on your moderation skills</li>
<li>There are three actions that can be performed on comments in your Comment Inbox: Archive (i.e. mark as read), Spam, Delete</li>
<li>When your Comment Inbox is empty, you can rest easy knowing you’ve dealt with all your new comments</li>
</ul>
For the history of this plugin, please see <a href="http://markjaquith.wordpress.com/2008/03/20/the-comment-inbox/" rel="nofollow ugc">The Comment Inbox</a>.

Comment Inbox

Enables a "Comment Inbox" that gives you the power of a moderation queue without having to manually approve every comment.

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.

Comment Inbox vs Comment Admin Notifier