You may well be thinking of the novel Today We Choose Faces (1973) by Roger Zelazny. The first-person narrator of the second portion of the novel is a member of a mysterious brotherhood of clones who all share access to a top-secret headquarters facility in which they keep "pins" which, if pulled, can download tons of old memories to any one of the clones who has grabbed the pin. The memories were apparently arranged chronologically -- pulling the first pin would give you, say, a bunch of old memories from the first fifty years (or whatever) of the brotherhood; pulling the most recent pin would give you the most recent fifty years' worth. (I don't swear it was calibrated in fifty-year increments; I just mention that to give you a rough idea of how it was organized. Like you, it's been a long time since I read the book, and my memories of it are getting fuzzy.)
I believe certain memories were automatically copied into the mind of each new clone when he was ready to go, and when one clone suddenly died, a psychic connection allowed an emergency download of his personal memories into the head of another (no matter how far apart they were, physically, at the time), but this still meant a lot of "ancient history" was simply stored at headquarters, available for access if unexpectedly needed again after being irrelevant for a great many years.
If you want to know more about the plot (including the "first half" that occurs centuries before the bit with the secret society of clones), you can follow the link I provided. It turns out that the Wikipedia entry for this book gives a detailed summary of the plot. On the other hand, if you'd rather not have it all "spoiled" for you, you might just try to find a copy of the book and reread it to see if the plot managed to give you some pleasant surprises the second time around.