I have, for some time, used the amazingly dexterous Rules module on my Drupal sites to receive email notifications when new comments were posted. I set up a Rule in the admin interface which would send an email if a new comment was saved on the site.

In the 'Message' section of the Rule's 'send email to arbitrary address' action, I would include a link to the commented-upon node, as well as the body of the comment text.

However, I wanted to also have a couple convenient links included: one link to allow me to quickly delete the comment (if the comment was spammy), and a link to edit the comment (sometimes I need to see the email address of the author, or change some wording if it's mildly inappropriate).

Luckily, Rules is well-acquainted with the similarly amazing Token module, so all I had to do was enter the following in the 'Message' (replacing what I had):

There's a new comment on the post [node:title-raw].
By: "[comment_author:user-raw]"
Commented-upon node: http://www.lifeisaprayer.com/node/[node:nid]

Comment Administration:
Delete this comment: http://www.lifeisaprayer.com/comment/delete/[comment:comment-cid]
Edit this comment: http://www.lifeisaprayer.com/comment/edit/[comment:comment-cid]

Simple, but brilliant. Rules could be described that way.

Note: Check out this drupal.org page for more advanced comment notification options.