Who's your all-time favorite player?
Mine is Mikhail Tal!

I suppose you want just one but I have to pick two. Fischer when I was young and Kasparov now.

Mine would have to be Bobby Fischer. I think I became interested in chess as a result of him. I do not know if I would have become interested in chess if he had not existed. 

Bobby Fischer and Emanuel Lasker.

I like Nomzowistch, Reti, Rubenstein, Capablanca, and plenty of others.  But Fischer and Lasker played like pit bulls pulling down a bear.  They simply would not let go.

Kasparov is awesome.  He may have been the best chess player of all time, and what he does politically is simply inspiring.  You can see http://www.kasparov.com/ or http://www.theotherrussia.org/ for more information about this.

What Bobby Fischer did in the first half of his life was also inspiring.  Unfortunately, this is not the case with what he did in his later years.

Tal and Bronstein.

Both geniuses who left legacies of beautiful games.

And both decent men who clearly played chess for the love of it rather than self-aggrandisment  - Tal would play pretty much anybody in offhand games and Bronstein played with graciousness in ordinary open tournaments.

 

Keres.  Best player never to be a world champion.  His games are fun to play through.  He had a plus record over Capablanca, Euwe, and Tal.  Also had equal records against Smyslov, Petrosian and Karpov.  Also beat Fischer a few times, making him the only player to beat 9 world chess champions.  

Ficsher

Kasparov - both for chess and his political work.