Great effort Sir Slasher (Marv) and thanks to Sir Litotes (Markus) for keeping track of weeks @ #1.
Of course, prior to 1973 (and even later), there were no global official weekly computerized rankings in terms of points given based on formula or assignments. Rankings were primarily decided by tennis journalists, promoters, and some player organizations, and that almost always happened at the end of the year. Some organizations did assign points based on the purse money for their tourneys. Even the so-called "computer rankings" were subjective to some extent due to the people who were assigning points to certain events. Many people just didn't see points given for numerous lesser tournaments where the quality was questionable as important as the performances in more prestigious tournaments. A Wozniacki type #1 would never happen in those days.
I think the ATP issued bimonthly "computer rankings" from 1973 up until 1977 or so. But these were also imperfect because they did not include many tournaments and events in their rankings, such as Davis Cup, WCT finals, the Masters or Masters Cup.
There were many years before the 1990's where the ATP computer rankings did not agree with the journalists or ITF end of year rankings. Heck, even the ATP itself contradicted its own computer rankings, for example, in 1975, where it made Arthur Ashe #1 instead of Connors.
It would take a lot of work, but what I would like to see is someone try to equalize the rankings points given over the years, based on today's points. In other words, assign historical tournaments as 250, 500, 1000, Slams , Davis Cup, Olympics and give the number of points based on today's values. I'm not sure it would be worth the work, but it would be very interesting.
But it's really difficult to equalize all things over the different generations. There was no requirement for players to participate in the tournaments as they are today. No such thing as required masters. Prior to the mid 1990's, many players, other than Australians, just wouldn't play in Australia because of the distance involved, travel and the timing. In the early years of the Open Era, there were other types of tournaments, such as invitational tournaments. There were winner-take-all matches that were by no means exhibitions. Many singles players played a lot of doubles.
The number and quality of players participating also made things different. Some years there were only 48 or 64 players in a slam draw and byes given like the Australian Open for example. Also, the Australian Open in those years and even in years prior to the late 1980's really almost exclusively consisted of Australian participants.
Most players had contractual agreements to play in certain tournaments or a certain number of tournaments. Sometimes these contracts caused them to be barred from other tournaments. Borg was barred from the 1977 French Open - Roland Garros because of his contract with the WTT (World Team Tennis).
In the late 60's and early 70's many players were under contract to the WCT (World Championship Tennis), or NTL (National Tennis League, later absorbed by the WCT) and because of that couldn't play in the French and/or Australian Opens. But then, Kramer and the ITF (or ILTF in those days) devised the Grand Prix Circuit with some 25-30 tournaments to counter the promoter contracts. Things got pretty bad in the early 70's and the ILTF and WCT were almost at war with each other, banning players from each other's tournaments.
So in 1972 (at the US Open), the ATP syndicate was first formed to try to protect themselves from the rival promoters and associations. But still in 1973, there were 4 rival pro circuits, the WCT, the Grand Prix, the US Indoor, and the European Spring Circuit, and in 1974, the WTT. Then later the WCT and Grand Prix merged for a while - about 4 years, before the WCT split off again and even had its own complex ranking system. Finally in 1990 the ATP tour was born uniting the players under one roof. But even the ATP has changed its handing out of ranking points over the years, most recently in 2009.