Instead of a "greatest single player ever", I like to think of it as the "best ever club". Chess is a game where even the greatest players sometimes lose. If there were a player who never lost, they would be the best ever. However there are lots of players who are not that far off and so I put them all into the "greatest" category.
My personal favorites are (Not in any order) :
Fisher, Tal, Kasparov, Capablanca.
Undoubtedly GARRY KASPAROV
Me!
Bobby Fischer!
Bobby Fischer!
Fischer at his peak--70 to 72--was the closest human we had to the top chess engines---his precision is what made him a man among boys
Fischer is the best---with Carlsen a close and closing second
i fischer--2 carlsen 3 kasparov 4 karpov 5 capablaca 6lasker 7 morphy 8steinitz
Well Bobby Fischer was(or rather to be precise...IS) considered to be one of the finest elite chess player so far.... There are legendary chess player who dominated their era...ex: Paul Morphy(maybe 150 yrs ago), Fischer...int the 20 th century...Kasparov, Tal........now Mangus Carlsen, the ever-fast Hikaru.. Vishwanath Anand....Karpov.... & the list expands just a s the growing universe...u see!
they say , chess is the only game the devil plays , so yes fisher by far , but the real question is why does the devil like chess so much , think about it 
1. Murphy, 2. Capablanca, 3. Fischer, 4. Kasparov, 5. Lasker, 6. Alekhine, 7. Tal, 8. Carlsen,
9.Karpov, 10. Philidor (or Steinitz)
Mikhail Tal, in his prime, at his best, for a short time, was the most brilliant player ever: "From July 1972 to April 1973, Tal played a record 86 consecutive games without a loss (47 wins and 39 draws). Between 23 October 1973 and 16 October 1974, he played 95 consecutive games without a loss (46 wins and 49 draws), shattering his previous record. These are the two longest unbeaten streaks in modern chess history."
Kasparov definitely is the best in the world