Very subjective, of course.  For me, it's really an apples and oranges comparison between the players on the list.   

Fischer's domination of the candidates matches leading up to his Wch bid against Spassky was one of the most remarkable accomplishments in chess history.  Objectively, I doubt that Fischer at his peak quite reached the same level as Kasparov at his.  It can also be argued that Kasparov's impact on the popularity of the game was no less than that of Fischer.  But Fischer's utter domination of the world chess scene in the early 70s, however brief, stands out in my mind.  For subjective reasons, Fischer gets my vote.

Too bad he lost his mind...

Alekhine and Morphy (another American tragedy) are also personal favorites who could arguably be considered greatest during their peak years.

A fun question, which has no answer that everyone can agree upon (I doubt we could even agree upon who should be on the list!).

OK I know I´ve probably left out people, but there is a limit of 10

Its Bobby for me -- many years on and he has still the 3rd highest all time FIDE rating, achieved without the current top players crutch of computer generated analysis. What more can you say - he revolutionised the GM approach to chess, took on the Soviet regime, etc. etc.