I spent several hours until I hit upon the solution I thought I would share this with anyone else having similar problems as I Googled a lot of similar questions awaiting answers. Drupal is running on Ubuntu Lucid.
/var/log/mail.log said that sendmail had "accepted for delivery" a Drupal-generated email from site's configured address: webmaster@babba.blogsite.org ... but that email never actually arrived
the mail command verified that mail could be successfully sent by another user logged into bash - and successfully received.
The problem turned out to be that "webmaster" wasn't actually a bash user on the Ubuntu machine.
It wasn't obvious to me that this was necessary and the sendmail was only installed with the intention to send from Drupal and not to receive.
The solution was to add a line in /etc/mail/aliases:
webmaster: root
I'm not sure how pertinent to the solution the /etc/hosts file is but I added these entries listing all the websites being served on the machine:
127.0.0.1 babba.blogsite.org iainhouston.dnsalias.net heplaysjazz.dnsalias.net localhost
Pertinent or not, /etc/hosts entries were not enough on their own.
I had installed sendmail and mail-utils into Ubuntu just for Drupal's use.