There are several reasons you might want to know the serial number on your Rolex Timepiece.  First, you might just want to know the exact model and manufacturing date of your Rolex investment for your insurance statement to protect yourself against loss or theft.  Perhaps if you need to send your timepiece in for service or modding, the Rolex vendor will want to know what they will be working on, in order to determine price.

Another and more specific reason is to determine the market value of your timepiece, either because you want to know its current approximate worth, or if you are considering selling.  Perhaps you want to upgrade to a different or newer model. 

Maybe when you were first starting out, you invested in a low cost Explorer I, which was in all steel. 

Not bad, but later on and many career advancements down the line you are ready to own your yellow gold Presidents Day Date or a hard to get Rolex Daytona.

Rolex Serial number engraved between the lugs.  Image from Bob's Watches.

The Rolex serial numbers are numbers with 4-8 digits and can be used to determine the date the timepiece was produced.  For many years the number was engraved between the lugs (the part/poles where the band attaches to the case) at the 6 o'clock position.  In order to find the serial number you would have to remove the watch band in the 6 o'clock position to see the engraving.  You may need a pin or a set of tools to remove the watch band carefully and return the band to working shape.  

Rolex engraves the serial number on the Flange at the 6 o'clock position on this Rolex Daytona.  Image from Bob's Watches