When I remote desktop into one Windows Server 2003 machine, I get a popup message saying "The security log on this system is full." When I open the Event Viewer, the security log size is 512.0 KB, which is the same as the Application and System logs. What is causing that message, and how can I clear the log to avoid it?
Right-click on the security log and select "clear all events". Optionally, save it off to somewhere else before doing so if you need to keep it.
To prevent it in future, check out either properties for each log (right-click/Properties) or a GPO: clicky. "Overwrite events as needed" was recommended to me by a Microsoft guy years ago.
MH's answer is a fine way to deal with the current issue, but someone needs to look at the logs regularly (weekly?) and check for issues/problems/etc.
See this question for an automated way to save/clear the logs. Backing them up is a good practice, useful for researching past issues and looking for patterns, etc.
The Windows defaults are nothing short of idiotic. Unless you're not really interested in the logs I suggest you set them to a much higher figure, such as 5 or 10 meg. Then set them to overwrite as needed. Bear in mind that when those logs are needed, and I mean really needed, it's often not the information from the last hour you want but the information from days or weeks back.