For an iMac, it's on the bottom of the iMac stand. Turn the computer off, turn it over carefully (lie it on a cloth, if you can), and you'll see it underneath.
If you can boot the computer, you can also find the SN in the About This Mac information - go to the Apple menu and click About This Mac. This works for any Mac provided that the logic board has not been replaced.
This works for any Mac provided that the logic board has not been replaced.
I recently had the logic board replaced in my iMac. After the tech left (on site repair thanks to Applecare), I went to about the Mac and found jibberish numbers. I called Apple and the AASP and found that he had forgotten to register the serial number. So he came back and, with a special tool (as he called it - looked a little like a USB stick) he contacted Apple and then entered my original serial number as I read it to him.
So, I assume they changed the process since I still have the same serial number as before.