The absolute minimum in maintenance is to check system and per-application log files regularly for error conditions and unusual events. Commonly, you will want to do this by writing a couple of administrative shell scripts and run them from cron periodically. The source distribution of some major applications, like smail or C-News, contain such scripts. You only have to tailor them to suit your needs and preferences.
The output from any of your cron jobs should be mailed to an administrative account. By default, many applications will send error reports, usage statistics, or logfile summaries to the root account. This only makes sense if you log in as root frequently; a much better idea is to forward root's mail to your personal account setting up a mail alias as described in chapter-.
However carefully you have configured your site, Murphy's law guarantees that some problem will surface eventually. Therefore, maintaining a system also means being available for complaints. Usually, people expect that the system administrator can at least be reached via email as root, but there are also other addresses that are commonly used to reach the person responsible for a specific aspect of maintenance. For instance, complaints about a malfunctioning mail configuration will usually be addressed postmaster; and problems with the news system may be reported to newsmaster or Usenet. Mail to hostmaster should be redirected to the person in charge of the host's basic network services, and the DNS name service if you run a name server.