It's an unashamedly unscientific approach, but take a look at who's name appears more times than anyone else's in the quoted text that's returned on the first page of this google search:
http://www.google.ca/search?hl=en&q=%22most+famous+chess+player%22&meta=
Now that I know the answer to the question - I would have to say Bobby Fischer!!! lol
However, because I am not familiar with Bobby Fischer's play (and I should be), I would have to go with Garry Kasparov!!!
Fischer was more controversial and he gained a lot of attention in the World Champion dispute against Spassky, then again, he gained much more attention refusing to play Karpov...
Right now the most famous and my favorite player is Carlsen, a 19 year old kid nicknamed "The Mozart of Chess", he gained the eyes of every chess player (including Kasparov, rofl)