Casual checks by system administrators is a good idea. There are auditing tools to give you a system status. Who, W and Finger give a list of all logged into the system. Net Stat shows services on the machine actually being used. Again look for weird host names and ports.
Log files can tell if people have been connecting to machines, log ins and log in failures.
Look for suspicious account names. Preventing Attacks Security vulnerability web sites are useful. Patches are important. Some platforms allow for automatic updating. Also important to keep in touch with security advisors for the various operating systems.