Almost certainly, Roy Emerson - at least as far as the men are concerned:
Emerson won 16 grand slam men's doubles titles - each of the majors at least 3 times, showing his all-around capacity to play on all surfaces.
He also was in no less than 8 winning Davis Cup teams for Australia.
In fact, even as singles grand slam titles go, he held the record at 12 titles for some decades before the record was finally broken by Pete Sampras.
Further, Emerson is the only male player in history to win all grand slam events, both singles and doubles ... and he won each of those titles at least twice!
In women's competition, the honour of the best of all-time would probably have to go to another Australian, Margaret [nee Smith] Court.
Court not only holds the greatest singles record of all-time, but won 19 grand slam women's doubles titles and 21 grand slam Mixed-sex doubles titles [2 of the latter were shared due to inclement weather preventing finals play-offs]. Some mixed-competition titles were also not held at certain Grand Slam events during her career; she almost certainly would have won more doubles majors.
As it stands, she is the only female player to win all 4 majors in all 3 possible competitions of singles, doubles and mixed doubles twice.
Probably her only rival for the title of best female doubles player in history would be Martina Navratilova, who won 31 women's doubles majors and 10 mixed-sex doubles major titles. She also won every possible major - but not twice.
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