From Remington's website, you can download and print a chart showing how to translate the two-letter code on the left side of the barrel at the chamber end into the month and year the barrel was manufactured. If the barrel has not been changed, that date should also apply to the gun itself.
Ed, I never remember seeing a serial number on an 870 barrel, but do remember seeing them on the receiver, left side. Just to be sure I checked the two I have in my safe. The first is an 870 TB vintage 1978 - serial number on the receiver, left side, none on the original barrel, just some proof marks. The second is an 870 Express, vintage 2005 or so, same story. I also have a slug barrel vintage 1980 or so, no serial number, and a barrel of unknown vintage that is marked "Full" and 3", but was damaged and cut off with a hacksaw. Same story, proof marks, some patent numbers, but no serial number.
The date codes for Remington are indeed on the barrel. I have a listing but don't have a scanner to post it here and is way to complicated to write down. If you can find the two marks on the left side of the barrel I will see if I can look it up. My TB for instance has the markings "LQ" which works out to February of 1978. I was able to obtain the table from www.remingtonsociety.com/rsa/questions/barrelcodes
The following serial number information is for
Remingtion firearms manufactured after 1921
Remingtons manufactured after 1921 have a code located on the left side of the barrel near the frame that identifies the year and month of manufacture. The following letters correspond to the months of the year, for example B=January, L= February and so on:
B - L - A - C - K - P - O - W - D - E - R - X
Barrel Code Location Diagram
Serial Numbers by date (factory record book)
1903 and 1903A3 Production and Serial No table.
B - Jan L - Feb A - Mar C - Apr K - May P - Jun
O - Jul W - Aug D - Sep E - Oct R - Nov X - Dec
M - 1921 N - 1922 P - 1923 R - 1924 S - 1925
T - 1926 U - 1927 W - 1928 X - 1929 Y - 1930
Z - 1931 A - 1932 B - 1933 C - 1934 D - 1935
E - 1936 F - 1937 G - 1938 H - 1939 J - 1940
K - 1941 L - 1942 MM - 1943 NN - 1944 PP - 1945
RR - 1946 SS - 1947 TT - 1948 UU - 1949 WW - 1950
XX - 1951 YY - 1952 ZZ - 1953 A - 1954 B - 1955
C - 1956 D - 1957 E - 1958 F - 1959 G - 1960
H - 1961 J - 1962 K - 1963 L - 1964 M - 1965
N - 1966 P - 1967 R - 1968 S - 1969 T - 1970
U - 1971 W - 1972 X - 1973 Y - 1974 Z - 1975
I - 1976 O - 1977 Q - 1978 V - 1979 A - 1980
B - 1981 C - 1982 D - 1983 E - 1984 F - 1985
G - 1986 H - 1987 I - 1988 J - 1989 K - 1990
L - 1991 M - 1992 N - 1993 O - 1994 P - 1995
Q - 1996 R - 1997 S - 1998 T - 1999 (*) U - 2000 (*)
V - 2001 (*) W - 2002 X - 2003 Y - 2004 Z - 2005
A - 2006 B - 2007 C - 2008 D - 2009 E - 2010
F - 2011 G - 2012
Using barrel codes (such as those listed above) to date the manufacture are reliable on Remington rifles, as the company rarely changed barrels on a customer's rifle.
Using these barrel codes to date a shotgun is somewhat unreliable, as shotgun barrels are often interchanged at random. One needs to be sure that the barrel is original to the gun before trusting the Barrel Code listing, above.
(*) On 8/9/99, stopped stamping the barrels with the date code. They continued to mark the date code on the end flap of the shipping box. They resumed stamping the date code on the barrel on 10/1/01.