Actually after hearing the "sent mail" sound so often, I opened the activity window and I see it says, "Outgoing messages" with a progress bar just prior to me hearing the sound, even when I am just reading mail and not sending. I have tried to fire up Wireshark to watch what Mail thinks it's sending, but so far no luck pinning it down. I can see that it is indeed sending mail, but based on the text, it looks to Junk mail and emails I have already sent. They appear to be going to the proper server and recipient, or moving to another mailbox. Most of my emails are PGP or S/MIME encrypted, so it's a little hard to tell, but looking at the SMTP headers it looks like it's just sending the identical email more than once. Because the message IDs are the same, I thought at first it was just an attempt to send something that failed, but in one case I had already received a reply to what Mail.app was just sending.
I am not an SMTP expert, but I assume clients or servers are ignoring these, since I have not received any complaints of the "you already sent that to me" nature. Bottom line - Mail.app is generating traffic I did not ask for, and sending mail when I did not press "Send."
I don't have Gmail or Outlook, just personal and work IMAP accounts. I am on Mountain Lion.