Kasparov. He achieved the highest rating ever, and was world champion for a very long time. Fischer was special in that he was able to defeat the Soviets, but he is just an "average" world champion, if that word can be applied to world champions. Kasparov is a standout, even among champions.
Who is the best player of all time?

Kasparov? Sure, he was good in his early career, but the wheels fell off a bit towards the end. He got anhilliated by Kramnik when he lost the world title, and, with all due respect to Kramnik, he isn't a world great. He only just saved the title against Leko and Topalov before losing it recently to Anand, none of which are phenominal either. Fischer, while undoubtedly great, has a fair bit going for him in that he was the American Cold war individual against the Soviets. I mantain Morphy is the greatest player. He played in an era where theory didn't exist as it does today, with none of the knowledge that later greats had. And he still managed masterpieces that are today considered some of the greatest games ever played. Fischer, for example, had his deep theoretical knowledge of the Najdorf Sicilian as one of his greatest weapons while Morphy had to make his moves based on calculation and intuition. Kasparov falls in the same boat, as, although he dominated the chess world for the better part of two decades, has not played the legendary masterpieces of Morphy, Tal or Fischer.

Tal .He is the most creative chess player eva and the greatest attacker the world has ever seen.Kasparov & fisher were great too...Hope they all were of the same time.that would have been the golden age of chess

Kasparov? Sure, he was good in his early career, but the wheels fell off a bit towards the end. He got anhilliated by Kramnik when he lost the world title, and, with all due respect to Kramnik, he isn't a world great. He only just saved the title against Leko and Topalov before losing it recently to Anand, none of which are phenominal either. Fischer, while undoubtedly great, has a fair bit going for him in that he was the American Cold war individual against the Soviets. I mantain Morphy is the greatest player. He played in an era where theory didn't exist as it does today, with none of the knowledge that later greats had. And he still managed masterpieces that are today considered some of the greatest games ever played. Fischer, for example, had his deep theoretical knowledge of the Najdorf Sicilian as one of his greatest weapons while Morphy had to make his moves based on calculation and intuition. Kasparov falls in the same boat, as, although he dominated the chess world for the better part of two decades, has not played the legendary masterpieces of Morphy, Tal or Fischer.
I disagree about Kasparov's greatness but putting that aside I'd like to say a few things about Morphy. Fischer was a huge Morphy fan. Not only did he say that Morphy "could beat anyone today [1964] in a set match," but as he studied his games he would at times analyse for half an hour to produce the correct response to a Morphy move--and Morphy seldom used as much as 5 minutes on any move.
Later on Fischer commented that he excluded himself from those Morphy would defeat. Vintage Fischer I guess.
On the other side of the ledger, Morphy was barely tested by his peers. The state of chess just hadn't evolved much excluding what Morphy himself had been doing. Closest to him was probably Anderssen who came to Paris well out of playing shape. Be that as it may; Morphy was the best player in the world and towered over almost everyone.

IBM's Big Blue... ZZZZZzzzzz......
are you sure about that????... how many world championships have been won by big blue

I would vote Fischer.look at his performances leading up to his champinship with Spasky. I don't have the actual numbers in front of me, but i believe he defeated Petrosian and another GM in STRAIGHT games with very few draws or losses. I will have to look up my figures, but he was the Babe Ruth, Michael Jordan of chess. It's just too bad he was apparently such a jerk as a human.
nobody is perfect.
Now,I too would Bobby Fischer because he did it on his own,chess wasn't mandatory to him as it was with the Russians,Cubans,or any other European country.But for many years I would say Capablanca was the greatest endgame player of all time.