The full answer really depends on what mail server program you are using.
For both the postfix and sendmail you can redirect mail addresses to local accounts using the /etc/aliases file: any line of the form address: unix-account will deliver email addressed to address@your.domain to the mailbox of unix-account. For example, if /etc/aliases contains a line like this:
postmaster: root
then UNIX user root will get all the mail addressed to postmaster@your.domain, without any need for postmaster to exist as a regular UNIX account.
Instead of a UNIX account name, you can specify the full path of a file -- mail will be delivered to that file (in mbox format). Other redirections are also possible; see man aliases for details.
Note: after editing /etc/aliases, you have to run the command newaliases (as root, typically) in order to have the mail server pick up the new addresses.