Philidor, Morphy, Capablanca, Tal, Fischer, Kasparov, Nakamura and Carlsen have all been described as players with towering natural talent.
I don't think there's any way to say who had more natural talent than the others. Fischer and Kasparov both combined amazing talent with an incredible work ethic to rise above a very competitive field. Before World War II, natural talent alone was usually enough to dominate the game.
Probably Mir Sultan Kahn. If he only liked the game more......
Some really good suggestions so far. Sultan Khan is someone almost nobody ever mentions.
Pity we are now away to see 25 pages of Fischer fanboys though. Could have been an interesting thread otherwise.
Always thought that as well as his awesome ability to create chaos on the board, the fact that Tal once went 95 games unbeaten shows he's one of the most naturally talented players ever. But agree with Rooperi And SmyslovFan (and Smyslov should also be on the list) - Sultan Khan an excellent pick.
Who creates fanboys. Of course, the media. Blame them.
Capablanca, a player I like a lot.
I always assumed that modern chess players, as talented as they are, still have a more sophisticated training than the old guard (so to speak).
I would say whomever invented chess had the most natural talent of any chess player.
Alekhine...
Capablanca or Morphy are my choices...they had far less compounded knowledge of theory, training methods or the talent pools others had to drive them...Morphy most likely didn't have seconds or advisors of any sort. In Capablanca's day, it was most likely more "mano y mano" than today also...
Pillsbury also...
The 3 anmes which spring to mind immediatly are Morphy, Capablanca, and Karpov. Each of them dominated their peers at chess, while working half as hard at it.
Possibly Carlsen as well. Too early to tell.
GM Jose Raul Capablanca 
There are countless numbers of players from the era of Soviet Union that have not been mentioned, and who deserve a place here:
Model (considered as even more promising than Botwinnik, but he died during WW2, I think he never played abroad), Stein (died from a heart attack before he was 40), Bronstein, Neshmetdinov, Keres.
And from today's chess: Nepomniastshi, Radiabov, Grishuk, Svidler, and of course, the incredible Morosevich and Ivanchuk (once here called 'Fumanchu').
(I was disappointed from Grishuk's colourless play in the candidates tournament. But the question was about natural talent.)
Players like Gelfand, Kramnik, Aronian... are considered as workoholics, but they showed a great talent early, too.
I think this question can have only a very subjective answer. Perhaps it should be modified to: 'Great talent AND early abstinence/disappearence/decline in play'.
There is a story about the 6 year old capa who was beating his father, who never even had shown him the rules of chess.
I think this is just another legend of a 'wonderchild', designed to raise the price in tournaments.
Later, people tried to confirm the legend by 'observing' an 'ease' with which Capablanca was beating his opponents.
In fact, part of the style of Capa was that his positional intuition failed rarely. This allowed him to reach situations where 'une petite combinaison' existed - often to the surprise of the audience, but I guess, to his own surprise, too ! - thus circumfering long complications.
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Beethoven was 'sold' by his competitive (and rude) father as a 7 year-old kid, in piano concerts, although he was already nine...
I'm glad someone added Keres and Leonid Stein. Sultan Khan has to be the most overlooked chessplayer to play at the top level. How about Akiba Rubenstein, David Bronstein, and Sammy Reshevsky? Sorry just noticed on re-reading some posts that Bronstein was mentioned.
Jehovah
Philidor, Morphy, Capablanca, Tal, Fischer, Kasparov, Nakamura and Carlsen have all been described as players with towering natural talent.
I think this list is nearly perfect, with the addition of Sultan Khan. The only one I'm not certain about is Nakamura. Why is he on the list? Is it mainly due to his USA records in becoming a master and a GM, or are there other reasons? I haven't actually heard that Nakamura was an extreme natural talent (relative to the super-GM level in which he resides, where of course being extremely talented relative to mere mortals is a given).
Another addition might be Blackburne, who learned chess at age 18, which is pretty much unheard of at top levels. Despite his late start, he managed to rise to the highest levels of chess at that time. Less than two years after learning the moves, he defeated Steinitz in a tournament game.
Forget chess theory and chess era. Who has the most natural chess talent?