When your computer systems are running smoothly, you may forget that it still needs to be monitored. Consistent monitoring may reveal hidden problems, or security breaches that would otherwise go undetected.
Your system logs should be checked regularly. On UNIX/Linux systems, these would be the syslog and messages files. On Windows systems, it would be the event viewer. These logs will usually have entries in them if hardware, software services, or applications encounters any problems. Some of these problems are transient, or are cleared up with a system reboot. Others can be warning that a piece of hardware is starting to fail.
Many times, when a drive fails, the logs will show that errors have been occurring beforehand. Often, in these cases, the system is able to recover from these early errors. They indicate that the drive is starting to fail. If these events are caught by checking the logs, then a repair can be made with the least amount of downtime, and the highest probability of avoiding data loss.
Another major issue that logs will reveal, is intrusions, or attempted intrusions. Your system logs will record all logins, and attempted logins, as well as other types of attacks like remote network connection, that are often used by viruses.
Consistent monitoring of your system logs can help spot these problems, and many others. It should be part of your regular tasks.