The greatest player

I voted for Kasparov because I think he would probably win a round robin tournament of the five given players (assuming we're pulling them through time at the moment when they were at their best and accounting for weaker opening theory, etc. in past chessic ages).

I think three of those players could be said to be the "greatest" in one sense or another.  Whenever I look at a Capablanca game, I always have to remind myself that the man hardly studied chess at all compared to modern grandmasters.  His natural understanding of the game was so good that he could defeat Dr. Lasker and become world champion while spending about as much time on the game as your average middling club player.  I think he had the best natural hardware of any chess player; his lack of study simply provided him with insufficient software.  Any of the other players on the list would almost certainly defeat him easily because they would be prepared.

Fischer had what I would call the best over the board intangibles, as well as a prodigy's natural understanding.  Fischer was a downright scary person to play over the board because you knew that in more or less EVERY SINGLE POSITION he was digging deep for moves that would kill you.  It's Fischer's killer instinct that made him so powerful, as well as his "styleless" play.  Instead of unnaturally hampering himself by adopting a certain "style" of play, Fischer was simply concerned with good moves.  His style was always whatever style was dictated by the position.  His all-consuming desire to win made him who he was, both before and after 1974.

Kasparov, on the other hand, has a- the best work ethic of any of the given players, and b- the best calculative ability and intuitive position analysis of any of the given players.  Importantly, he was not born with the ability for deep calculation, nor was he born with the ability to analyze and understand with lightning quickness the essentials of the game.  He did the best job that any chess player has ever done of coming to an understanding of the game.  That is why he consistently won (and won big) over the world's very best for two decades straight, and that is why he would go 4-0 against the field of Fischer, Alekhine, Capablanca, and Anand.

-Caley