Since the 1870's (but with some explanations until the 1960's
Of course my list could change a little in future years when I will have collected more results and have made numerous new analysis.
Sorry for not listing women but I'm not competent at all
1876-1879 men: 1. Hartley, 2. James Dwight, 3. Hadow
1880's men: 1. W.C. Renshaw 2. J.E. Renshaw 3. Lawford
1890's men: 1. Joshua Pim, 2. R.F. Doherty, 3. Wilfred Baddeley
(4. M.D. Whitman)
1900s men: 1. H.L. Doherty, 2. W.A. Larned, 3. R.F. Doherty
(4. Brookes who had a top career which started in the mid-1900's and ended in the mid-1910s)
1910s men: 1. Wilding, 2. Johnston, 3. R.N. Williams (?)
1920s men: 1. Tilden, 2. Cochet or Lacoste (4. Johnston)
1930s men: 1. Vines, 2. Perry, 3. Budge or Nüsslein (5. possibly Tilden)
(Budge was the greatest of the three if we judge their entire careers but in the 30's Budge was "absent" until 1934 included)
1940s men: 1. Riggs, 2. Budge or Kramer
(there is no doubt that Budge and Kramer were better than Riggs but if we select only the years from 1940 to 1949, Riggs was the best in particular because Budge injured in 1943 and Kramer was not a very great in the first half of the 40's)
1950s men: 1. Gonzales, 2. Segura, 3.Kramer
1960s men: 1. Laver, 2. Rosewall, ... 3. Gonzales (4. Gimeno)
1970s mens: 1. Borg, 2. Connors, ... 3. Nastase
1980s men: 1. Lendl, 2. McEnroe, 3. Wilander
1990s mens: 1. Sampras, 2. Courier or Agassi
2000s men: 1. Federer, 2. Nadal, 3. Hewitt
60's : Gonzales was possibly the best in 1960, was #2 in 1961 at 90% (or #1 at 10%), #3 in 1964 (and could have finished at #1 or 2 had he played the South African pro tour) and from 1965 to 1967 in the pro ranks didn't play much and in particular didn't enter most of the majors but on one tournament could beat everyone and if we compare him with the best amateurs in 1967 he beat Stolle something like 5-2 in direct meetings, Stolle being close to the amateur #1 spot in 1966 (Emerson, Roche, Stolle and Santana were all very close that year) with his wins in the Davis Cup, the US amateur and the German amateur. In 1968 or 1969 he was still able to win events equivalent to the Super 9 or Masters 1000 (Pacific Southwest and Howard Hugues Open in 69).
Gonzales was better than Gimeno in 1960, 1961, 1964, 1965, 1968, 1969 (Gimeno was better in 1962-1963 because Gonzales only played 1 match in 2 years and was better than Pancho in 1966-1967 only because he played throughout those years while Gonzales only played half of the time but in direct meetings Gorgo continued to dominate Andres).
When Gimeno played the same circuit than Emerson, Gimeno was slightly better than the Aussie, be it in 1960 (until July) or in 1968 and 1969 so we can guess (but I recognize it isn't a proof at all) the Spaniard was better than Emmo between late 1960 to 1967. We can also guess that in 1966-1967 Emerson and Stolle were close. In 1967 Gimeno had always better results in the pro ranks than Stolle (except in the South African tour in September) and in direct meetings Gimeno beat Stolle that year 8 matches won to 2. In fact in 1967 Gimeno was very close to Rosewall and Stolle was less good than Laver-Rosewall-Gimeno and even Ralston in the pro ranks. So it is very likely that in 1967 Gimeno was superior to Emerson assuming that Stolle and Emerson were close that year (I recognize a great hypothesis).
Gimeno was never the #1 in any given year in the 60's but he greatly rivalled the best pros (for instance in 5 years (1963-1967) Gimeno won 22 tournaments where he beat either Laver or Rosewall and in particular 7 tournaments where he beat both giants. I don't think Emmo would have been able to do that). When Gimeno and Emerson played again the same circuit in 1968 both had equivalent results but Gimeno led 6-2 in head-to-head that year.
In conclusion I don't even see at all Emerson in the Top4 of the sixties. I think that in his very best years Emerson was at best the #4 in the world.
Emerson certainly not : in his best years he was never in the Top3.
Last remark about the 60's :
From 1960 (French Pro) to 1971 (Australian Open) among the 31 majors (here I take into account the 3 Pro Slam tournaments, Wembley-French Pro-US Pro, from 1960 to 1967 and the true Slam events from 1968 to 1971 (I slightly get beyond the pure 60's) where either Rosewall or Laver entered (so it includes majors where both players entered) 29 of them were won by those 2 giants of the game. Astonishing: Rosewall won 16 such majors in that period and Laver won "only" 13... Only Ashe (US Open 1968 ) and Newcombe (Wimbledon 1970) could break that gigantic series!
The advantage of this list is that we have always the same events (at least from 1960 to 1967) but sometimes one of these events hadn't always very strong fields.
If I pick up in my own list (which is of course subjective and therefore debatable) of the 4 greatest events of each year of the 60s (see
http://tt.tennis-warehouse.com/showpost.php?p=2840980&postcount=45 and
http://tt.tennis-warehouse.com/showpost.php?p=2840980&postcount=46) :
Rosewall won 17 or 18 of them, Laver 17, Gonzales 4, Ashe 1 and Hoad 0 or 1. It is probable that I underrate a little bit the amateur players's feats but I don't think too much.
Of course we can't judge players only on their results in majors because many other criteria (proposed by members of that forum such as urban, jeffrey, and others) shall be used (number of years No. 1 (but some years the #1 is unclear), dominance during peak years, head-to-head records against contemporaries, number of tournaments won (including pro match series), number (and percentage) of matches won/lost (consistency), number of Masters, Super Nine events and their equivalents, consistencsome extra points for different surfaces, especially grass and clay (for versatility),
quality of opposition (the most difficult criterion to rate), etc...).
But when you see how much both Aussies dominated the others in majors there is no doubt at all that Rosewall and Laver were clearly the Top2 of the 60's : neither Gonzales or Gimeno or Emerson are in that Top2.
For the moment I consider Laver as the "top banana" of the 60's but given the last statistics written just above there is a little possibility that Rosewall was perhaps the top player of the 60's.
see the 1970's to 2000's below