They have date code stamps on the barrel which can be looked up on the manufacture date link on the Remington Society of America.
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Update: It's important to note that the barrel on the shotgun MAY not be the barrel that was originally on the shotgun at purchase. Check the serial number with Remington.
100-350 USD
Made by the Remigton Firearms Company.
Serial 718943w
The W ahead of the serial number indicates that your Remington 870 wingmaster was made in 1972.
They are all still made in Illion, New York, I believe.
Check this table for the answer: http://www.remingtonsociety.com/rsa/questions/barrelcodes
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
You can call Remington at 1-800-243-9700 and go thru the menu selection. One of the menu options is to request information on your Remington based off of the serial number.
Remington Society barrel code lookup: http://remingtonsociety.com/rsa/questions/barrelcodes
Go to the Remington Society of America and click the Manufactured link, it has the location and barrel codes for month/year of manufacture.
See related link.