Let us say you have bought a new Mac System and you want to register the system with apple for future upgrades. Apple would request you to enter your Mac serial number for the registration. You can quickly find a Mac OS X serial number using the About this Mac menu option.
On clicking the About This Mac menu would display the following
To see the serial number of your Mac, click the More Info button.
The above dialog has the Serial Number (System) of your Mac System
Update – Demo Video on Mac OS X Lion