Greetings,
What a question!
Before giving my own answers(!), I must define both the word "greatest" and the criteria for deciding who is the "greatest".
If one simply looks at
natural playing ability, independent of studying books as most players do, then the greatest player, in my view, is
Capablanca. He only studied the endgame - the openings and middlegame play was acquired over-the-board. Not bad for someone who was "lazy" and relied purely on his talent!
If one could somehow bring all the players together without their "book-knowledge", I don't believe that there was - or is - anyone who could compete on his level.
If one looks at
tournament/match results, then
Karpov is surely the "greatest".
If one looks at
dominance - well, that's a challenging choice between
Fischer and
Kasparian In this context, I mean the "intense will to win (crushingly!)".
The problem with Fischer is that, but for a mere handful (if that) of home-grown American players, in the US he was a shark in a minnows' pool. It's only in his stunning run of crushing victories against the Soviets in the Candidate Matches and his victory over Spasski (from a 0-2 deficit) that one sees what his potential ability to have had a long reign might have been.
It's difficult to say who might have won between him and Karpov - I think the latter would have been too mentally-strong and well-prepared to lose to Fischer. For his part, Fischer's "psychological warfare" leading up to the abortive match may have worked against himself more than Karpov.
As regards a match between Fischer and Kasparian at their respective best ... there'd have been "fire on" more than "the board"!
In terms of
creativity, the choice is between
Tal and
Kasparian.
In terms of
longevity, then
Lasker's your man - although that may seem to cheapen his accomplishment(s). I've always had a deep admiration for him - for both his academic achievements and his seeming ability to turn-around games with astonishing regularity. I've yet to read (or buy!) Soltis' recent book on him...I certainly would like to do so - unless someone's already read it and could tell me what was Lasker's secret??
It was said that he played like a "black magician", his escapes were so numerous. Of the "Big Three" - Lasker, Capablanca and Alekhine - he seems to have been the only one to actively use psychology as a factor in his games.
For example, he often took advantage of Janowski's
penchant for a particularly bad pawn structure along with the two bishops - by exchanging both his bishops for the knights on c3 and f3, resulting in the weak pawn-formation, c2, c3, d4, e4, f3, f2.
He would then win every game against Janowski with this setup - without the latter ever understanding how he managed to do it!
As an aside, the talk about Morphy dropping pieces/blundering...
I think that this was more a case of his losing interest in a game whilst having had to wait for his opponent's move. I take the fact that he moved quickly as an indication of the level of his mental faculties as regards chess.
Rather like a very bright child at school who becomes bored and (self-)destructive because the other children are taking so long to grasp what he's already grasped.
His experiences with other players might well have contributed to his early "retirement" - if only he could have played Capablanca and Karpov; players who moved at the same pace as him!
Kindest regards,
James