They have date code stamps on the barrel which can be looked up on the manufacture date link on the Remington Society of America.
---
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
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.
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
Go to the Remington Society of America and click the Manufactured link, it has the location and barrel codes for month/year of manufacture.
Remington Society barrel code lookup: http://remingtonsociety.com/rsa/questions/barrelcodes
See related link.