Seems to be asked quite a bit so I thought I'd help a little in this regard. Don or Sherm might jump in on this but pictures speak a thousand words they say. Most know the most logical place is a plate on the motor
First one is more of a distance shot to give you an idea - most I know are on the starboard side of the motor
and a close up view of what that tag could look like (info on tag may vary)
and then if you can't find that - look for the welsh plug as it'll be stamped on it
Remember its Digit, Letter, 6 more Digits (except older motors) and rebuilt motor may not have the serial number.
Remember - Mercury DOES NOT go by year but by serial number when it comes to ordering parts etc.