Typically, noreply addresses are used as a blackhole for mail that probably won't be replied to, and any replies are either auto-generated (e.g. mail delivery failure notices), spam, or other undesirable mail.

I have seen a good compromise for this, though: a piece of software I use sets the sending address to "noreply.support@mydomain.com"; if you want to reply to the message (and you aren't a spammer or mailer-daemon), you simply delete the "noreply." from the beginning.