Someone whose clue-bit is set will also install some security patches, but that tends to be the limit of the attention to the system. For the time being, I'll give you a run-down on some of the biggest issues to consider, which should cover the most common cases. Install Security Patches Script kiddies can break into computers because people do not install patches on their vulnerable systems. Security patches are upgrades to the locks on your server. I cannot stress enough how important it is to have all of them installed.
New bugs pop up and new patches are released on a regular basis.
Watching lists like Bugtraq and Web sites like rootshell isn't a bad idea either. Often, problems discussed in advisories are analyzed in these types of media long before patches arrive. This has been said time and again, but a majority of the break-ins we see could have been avoided if unused services had not been running. If not, make sure sendmail isn't running. If not, make sure that imapd isn't running.