By serial only by calling remington, however they are date code stamped on the left side of the barrel in front of the receiver. Lists are less common, mostly don't exist (publically availably) once they started being date stamped in 1921.
Serial numbers by year for the 870 Remington Model.
Serial 718943w
D081337n
I think only Remington can tell you that if you call OR you could go to the Remington Society of America and look up the barrel date code here: http://www.remingtonsociety.com/rsa/questions/barrelcodes
The W ahead of the serial number indicates that your Remington 870 wingmaster was made in 1972.
Go to the Remington Society of America and click the Manufactured link, it has the location and barrel codes for month/year of manufacture.
From the date code stamped on the barrel. Look for the manufactured date link on the Remington Society of America for details.
Not without more information
Check the manufactured date link on the Remington Society of America for details.
The month and year your gun was manufactured is......december of 1965 Hate to disagree but that simply cannot be right, they didn't even introduce the "Express" (lost cost 870) until 1987. I would check the barrel code date stamping, the information about this is on the Remington Society of America, see related links for it.
Look at the date code stamp on the barrel, see related link.
Do a search on barrel codes, I believe that will give you an answer