At first glance, there doesn't seem to be anything special about the MyDoom virus compared to other viruses: it arrives via email as an attachment, and has no effect unless the user, running Microsoft Windows, opens the attachment; if the user does so, it sends itself to other email addresses it finds on the user's computer. It uses no new technological exploits, though I think the social exploit of saying, "The message contains Unicode characters and has been sent as a binary attachment," to encourage recipients to open the attachment is a tad more clever than usual. It searches for email addresses in all kinds of files on the user's hard drive, and sends itself out using a built-in mail server from forged sender addresses— not sure if those are new techniques, but they're also a tad nifty. If the user has the Kazaa P2P file sharing program installed, it will also share itself under inconspicuous but potentially popular filenames.
I'm used to getting a little splash from each major Microsoft Outbreak at work, but today we just got hammered. The message was sent to my pager several times today. I've had several dozen messages sent to my personal email account, though some of them are bounce messages generated by the virus trying to send mail in my name, as random addresses under this domain name. All in all, quite the little show.