Paul Morphy.
Who is the best chess player of ALL TIME?
Well, it depends on your criteria for "best". Here are some of my votes, although there are others who can arguably beat any of these in their category:
Highest rated? Magnus Carlsen
Most dominant? Garry Kasparov
Most brilliant? Bobby Fischer
Most influential? William Steinitz
All of the above? Philidor (the Babe Ruth of chess, perhaps)
The issue with Carlsen is that his only real claim to greatness right now is his rating. Unfortunately, there are serious problems with relying on ELO as the final arbiter of greatness so I think the verdict of history is yet to be decided on him.

(1) Fischer (2) Capablanca, because he lost fewer game than any grandmaster, 46 loses is not bad for a player playing all his life. (3) Kasparov (4) Karpov and (5) Carlsen, he need to improve it in his next world champoin match this year, if he wins, maybe third place. (6) Alekhine, because he is my hero and great player. :)

Agree on Carlsen. Another strong candidate (compared to their peers) would be Rubinstein due to the fact that he had an astounding grasp of rook endgames.

Well, it depends on your criteria for "best". Here are some of my votes, although there are others who can arguably beat any of these in their category:
Highest rated? Magnus Carlsen
Most dominant? Garry Kasparov
Most brilliant? Bobby Fischer
Most influential? William Steinitz
All of the above? Philidor (the Babe Ruth of chess, perhaps)
The issue with Carlsen is that his only real claim to greatness right now is his rating. Unfortunately, there are serious problems with relying on ELO as the final arbiter of greatness so I think the verdict of history is yet to be decided on him.
The standard of playing strength has gone way up so a Fischer like domination of one's fellow super GM is unlikely to be repeated due to today's super GMs having better defense, technique, and calculation. The ability to convert a small advantage into a win is critical even at club level. As for the opening even beginners are well prepared and memorize their pet lines 20 moves deep, contrast with many of Alekhine's games from his best game collection where he openly admits to making opening "mistakes" (usually just inaccuracies) relatively early.

I would imagine Kasparov would be worthy of a shout.
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Must we get emotional? lol ^^^^@#14
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most handsome world champion:Capablanca, greatest womanizer:Spassky,most fanatically dedicated to chess:Alekhine,Fischer, Greatest stamp collector:Karpov, most unpleasant personalities:Alekhine,Fischer,Botvinnik best paid of all time:Fischer,most loved by chessplayers:Tal most dry kind of play:Botvinnik,Karpov,Capablanca most fiery:Tal most influential:Steinitz, best defensive geniuses:Petrosian,Lasker most fierce attackers:Tal,Alekhine,Kasparov Greatest natural players:Capa,Anand,Carlsen
Probably Magnus Carlsen