I suppose you want just one but I have to pick two. Fischer when I was young and Kasparov now.
All-time favorite player
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.

i love the way Paul Morphy played. Very very quick on almost every move and hardly blundered and excellent positional player. Would be tough to see him lose a blitz game.
I find a lot of enjoyment in going through Mikhail Tal's games. Just when you think the position is becoming simple and slow...WHAM!! A spectacular piece sacrifice that almost ends the game right there. His ideas will amaze me forever.
I agree. Karpov is also a very strong player. One of the greatest positional players ever; it's a shame he's not active.

I agree. Karpov is also a very strong player. One of the greatest positional players ever; it's a shame he's not active.
Hi is active, but not so much.

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.
I would agree that Keres is a very strong player, but no one played with as much determination as Korchnoi. Playing two world champion events while your family is in prison against arguably one of the strongest positional players of all time is a feat unto itself. That is why I give the slight edge to korchnoi, but also do not wish to say that Keres was any less of a player.
Who's your all-time favorite player?
Mine is Mikhail Tal!