How to create a rule to notify administrators of new comments by non-administrators? I would like to use Rules to notify all administrator users of new comments that have been posted to the site.

I can get as far as getting the notifications working for all comments, but I would like to set it for notifications to just comments by non-administrators. Administrators will then not be notified for their own responses to comments.

Any hints?

Note: I want to do this so that I just have to specify the admin role only, as many new roles will be added that are non-admin roles. This way I do not have to update the rule every time a new role is added by site admins.
What you are trying to do is pretty straightforward. I suspect that you have a Rule that is active and has the following:

On event After publishing a comment

(no condition)

DO

Send an email to user (or whatever you want to be your notification method; it doesn't really matter)

What you need to do is add a condition by clicking on the respective option. In the "Condition to add" option, you need to select: "User has role(s)" and press Next. 

In the next page, select "Published Comment Author" in the User option and select all the roles of your site except for the Admin role. Leave the rest unchanged.

Now your admins should be receiving notifications for comments from non-admins only.