Any time you get yourself a new bike (new to you, doesn't matter if it's brand new or previously enjoyed). Always take a moment to write down the serial number. I personally keep a spreadsheet in google documents that I can access from anywhere including my phone with all my major serial numbers.
In the unfortunate event of a theft, you want to be able to very quickly find that serial number and provide it to the police and local pawn shops. The quicker you can get the serial number out there the more likely you will be to catch them when the thief tries to fence the bike.