As with any other security barrier you put in place to protect your server, it is pretty tough to defend against untold damage caused by someone with physical access to your environment, for example, theft of hard drives, power or service disruption, and so on. Therefore, console security should be addressed merely as one component of your overall physical security strategy. A locked "screen door" may deter a casual criminal, or at the very least slow down a determined one, so it is still advisable to perform basic precautions with regard to console security.
The following instructions will help defend your server against issues that could otherwise yield very serious consequences.
First and foremost, anyone that has physical access to the keyboard can simply use the Ctrl+Alt+Delete key combination to reboot the server without having to log on. Sure, someone could simply unplug the power source, but you should still prevent the use of this key combination on a production server. This forces an attacker to take more drastic measures to reboot the server, and will prevent accidental reboots at the same time.
To disable the reboot action taken by pressing the Ctrl+Alt+Delete key combination, comment out the following line in the file /etc/init/control-alt-delete.conf.
#exec shutdown -r now "Control-Alt-Delete pressed"