I assume Michael Concordia was asking about the show's ending
music and not the opening theme, "Those Were The Days."

According to the Archie Bunker Fan Site, the name of the ending
tune is "Remembering You" by Roger Kellaway and Carroll O'Connor.
See http://www.webspawner.com/users/abunker/factsandquestions.html

Joyce Brite
Player Piano and Mechanical Music Exchange
http://mmd.foxtail.com/Exchange/