Relative strength compared to his contemporaries : Paul Morphy, no question. If he had access to the amount of theory modern players have today, he'd be giving knight odds to 2200 players.
Very good. I've argued that if Morphy had been born 20-25 years ago instead of 180 (and assuming of course that he would pursue a professional chess career), he would be one of the best if not the best today. And based on his natural talent, I believe he would be the best.
Paul Morphy was the most naturally talented player that ever lived.
Bobby Fischer was the strongest player that ever lived during his 1970 - 72 playing days.
Garry Kasparov was the strongest player ever for a block of time longer than 5 years ( sorry Bobby ).
Magnus Carlsen.... recently started predominantly wearing glasses now.
I think Morphy was the greatest in history on relative basis (as I explained in my opening post).
I agree that he was also the most naturally talented. I might rank Capablanca second in natural talent.
Fischer was totally dominant during the '70-'72 period, but it was just a three-year period in a 20-year career.
Kasparov was certainly one of the greatest but if you're considering dominance over a long period of time, what about Emanuel Lasker? Remember, the point of this is not absolute strength, but rather relative strength.
So what's your nomination for greatest of all time?