In which sendmail configuration file are the domains listed that the machine is responsible for serving?

(Specify only the filename, without the path.)

Answer: local-host-names

Explanation:
From http://www.faqs.org/docs/securing/chap22sec180.html:
The /etc/mail/local-host-names file is read to obtain alternative names for the local host. One use for such a file might be to declare a list of hosts in your network for which the local host is acting as the MX recipient.