Since the National Archives and Records Administration (NARA) of the USA administers Presidential Libraries, a query to NARA might be useful, if only to find out if NARA knows of archived or compiled lists by President, perhaps, and/or if these types of correspondence/records were/are felt important enough to be officially preserved. In the Johnson Library, for instance, the list of holdings of Presidential papers includes "PRESIDENT'S NIGHT READING AND SIGNING TABLE LISTS" which sounds as if it should include anything he signed "each day". (PAPERS OF LYNDON B. JOHNSON:
PRESIDENTIAL PAPERS See Section V - Special Files. http://www.lbjlib.utexas.edu/johnson/archives.hom/holdings/presiden.asp )
And, since you mention this happens also in other countries, here in Canada, Her Majesty Queen Elizabeth II [/I] will send messages to Canadians who are 100 years of age or older and couples who have been married for 60 years or more. Canada's Prime Minister will send certificates for 25th wedding anniversaries and up (at 5-year intervals) and for 65th birthdays and up. There are other levels of recognition from the Governor-General, provincial Premiers, etc. I just sent a note to the Prime Minister of Canada to ask if copies or lists are kept, made public, or saved as official correspondence or in the Archives. Also I asked what year this programme started. I suspect it was done only informally until maybe mid 1950s but could be wrong. I once read through a few years of our very first PM's outgoing correspondence and don't remember seeing any! I did not get an answer on the history on the programme, but the message I received from the current Prime Minister of Canada's office says this information is a "private issue".