Yes, the e-mails you describe are most likely the latest e-mail worm virus MyDoom, or one of its variants. This virus raids the address box of a victim machine, randomly selecting pairs of addresses. It uses one of the pair for the originating, and the other of the pair for the destination, address of a new e-mail which it then sends. This new e-mail is, of course, a virus vector, and this is what you are seeing in your address box. The payload is located in the attachment(s) of the vector e-mail which masquerades as a failed mail message. The text of the vector usually has some enticement to open the attachment, for instance a claim that the attachment contains information on why the purported (but non-existent) message was not delivered, or the first N lines of the message. This should be your second clue (after the fact that you don't recollect sending the supposed failed message). No mail server that I am aware of puts its explanation for failed delivery in an attachment. They all put the explanation in the text of the e-mail. As long as you do not open the attachments you will be perfectly safe. You should, of course, delete the vector e-mails that show up in your inbox, (make sure that the attachments are being deleted with the messages). Should you open the attachment, one of a number of things might happen (there are several variants now that do different things), but the most disturbing thing is that the virus installs a keyboard shim which intercepts and stores key strokes before they reach your operating system. Thus passwords and any encrypted message or file that you type are stored in plain text and are available to any hacker who has a key to the MyDoom back door. This virus is also associated with zombie denial of service attacks directed against SCO and Microsoft. I'm not sure if this is coordinated by the virus itself, or by some ancillary software that takes advantage of the backdoor created by the virus to coordinate a mass denial of service attack. In any case, it seems that the hackers don't have enough to do once again, and we users will be victimized if we don't stay sharp and informed.
Ed: "Users? Stay? Sharp? Informed? You've got to be kidding!"
"Ed, it's on of those rhetorical things; I'm sure you wouldn't understand."
Reality: An important truth test