If you are having a force.com site or customer portal and do some kind of self service portal, one of the things you would like to do is to provide a do-not-reply email on your email templates. This is meant for customers not to reply to auto generated emails and follow the process instead of spamming with requests. Now is this the right customer service you want to do is a discussion by itself. So How do i make a do-not-reply email on email templates for anonymous users of my site?
The solution
a. By default, salesforce creates a guest user for every site you create on your org. All you have to do is change the email id of the guest user to a do-not-reply email , change the display name to a valid name.
b. IF you want all the emails generated by salesforce to have a donotreply email, then go to customer portal settings and change the from email id and display name to have a global change.

How to do it
a.If you go to setup, sites and click on the site label, it would go the site detailed page. Click on public access settings and click on users. Now this would display only one user who is the salesforce generated site user for your website. Click on edit and change the display name to a valid name and from email id to do-not-reply email id.
b. Now this would override any email display name you use on your apex code. So if you are sending an email on a forgot username/password scenario, and use setDisplayName method , the above settings will override it.

Please feel free to comment your thoughts on the posting and any questions you have and i will be glad enough to answer it for you.