UPDATE (24 September 2010):
There is some interesting discussion on this very topic on Hacker News at: http://news.ycombinator.com/item?id=1723421 about this article No company should ever have a noreply email address by Ryan Waggoner.
Joel Spolsky makes a compelling argument in favor of No-reply address here – That no-reply addresses should be used on a case by case basis since there is a financial cost to the recipient.
I still believe that ridding of no-reply email addresses is worth it to more companies that others, especially ones who are sending to paying customers. If GoDaddy sends me an email about an automated charge on my CC, I should most definitely have the ability to reply to that email. The pain caused to me, fumbling through their site in order to contact the correct department, even though they just emailed me, costs more to me than 10 cents. And it costs them because I am pushed to no longer be a customer. Personally I would pay 10 cents if it meant holding a customer longer.
I think my RescueTime example below was not the best and what really prompted the post was this interaction I had with GoDaddy. It just so happened I received a no-reply email from RescueTime right after a frustration I had with GoDaddy and honestly I a bit surprised by it.
I think people are replying to these emails in either case, so why not, at the very least, take a look at a few instead of shutting your eyes from them.
I don’t know about you, but I do not understand “no-reply@_____.com” email addresses.
Common uses of this you see are with account validation and report summaries. So, for example, when RescueTime emails my weekly efficiency report to me, I cannot reply to the email. Should I have a question or even a suggestion for them, my reply, presumably, will go into oblivion.
How high could the cost be to “deal” with people replying to such an email? Why would you want to miss out an opportunity to interact with your customer?