Mossberg, Stevens, Savage , Cooey and probably others as well did not put serial numbers on their firearms until US law mandated it in 1968, as was mentioned above. I have owned several with no serial number, and as was also mentioned earlier, the CFC will issue you a "Firearm Id Number" and a sticker with that number on it to attach to the gun. In my experience they don't stay stuck on for long. The CFC will send you replacement stickers though if you request them. They once re-issued me duplicates of all of mine because I was having issues with them falling off and wanted spares.
Jim