Most do, some don't.
It would have to be on the receiver to comply with Federal Laws. But keep in mind that firearms did not require to have serial numbers on them until the "Gun Control Act of 1968". So if your firearm was manufactured prior to that year there was no requirement for it to have a serial number. Most firearms made prior to '68 do not have serial numbers. (All Savage Fox model B shotguns were manufactured pre 1968) Here is a link to some very good information about these shotguns: http://www.chuckhawks.com/fox_B_shotguns.htm
You may not be able to date it to a specific year, but MAYBE to a range of years. Serial numbers were not required by law for rifles and shotguns until 1968- so we know your rifle is pre-68. Beyond that, we may know that a given make and model was only made from 1949-1954, so we can narrow it down that much. Sorry-
My best guess is sometime between 1962 (When Sears signed a contract with Ted Williams) and 1978 (Sears discontinued the Ted Williams markings that year), The rifle is a Winchester Model 70- excellent rifle, by the way. The 273 number is the model number. If there is no serial number on the frame, it was pre-1968 (serial numbers were not required by US law on rifles and shotguns until 1968)
It was made by mossberg or savage for montgomery ward. I'm guessing the m means it was made by mossberg and if it doesn't have a serial number it is pre 1968 because mossberg didn't put serial numbers on their long guns pre that date.
Remington Model numbers are normally on the left face of the receiver. Early shotguns and rifles did not have a model on them at all. Like for example the early Model 11 shotguns which I suspect you have if it doesn't have a model. probably pre-20's need serial to know.
It is pre 1964 with a serial # of 496507
Browning website, customer service, look up the serial number of your A-5. No records available for pre-war shotguns.
Russell Arms was used by several makers in the 1890-1915 time period. If yours is a "top break" gun, remove the forearm, then open and remove the barrels, and check the frame under where the barrels close. However, you may not find a serial number. They were not required by US law on rifles and shotguns until 1968. Perfectly legal to own a pre-1968 gun that never had a serial number. Highly illegal to REMOVE a serial number.
pre '64 is based on serial numbers under 579600
not sure when they were manufactured, the two i know of, neither one has serial numbers. so pre 64. one I'm trying to buy is a double barrel 12. sorry i didn't have anymore info.
The pre 1969 model 60 didn't have serial numbers so if you can't find the numbers it's probably pre 69.
Before '68, serial numbers weren't required, so it may not have one. However, if the pistol grip is checkered it is a pre 45 if not it is pre 68