Reboot the Linux computer (CTRL+ALT+DEL should be able to to this gracefully for you without having to log in)
At LILO key in linux S (you may need to press CTRL+X to get to the text based LILO prompt).
Note: Once the Linux loads up into Single user mode, it will drop you to a Bash# prompt. It will not ask you for a password.
You may then type "passwd" to set a new password for root.
Type "exit" to reboot the server.
Contratulations, your root password has been reset!
Additional Information
This functionality can be changed. Also, this method relies on physical security - if they can reset your password using this method, they can just as well send the computer out the window and crashing to the ground. It's all about physical security.
LILO could be protected through the use of the restricted keyword.