What is Kasparov's greatest game of chess? His most epic? His most brilliant? His most accurate contest, maybe by both parties? His best ending? His best attack? (The number of possible categories is almost endless.)

what? move 24, rook for pawn. understandable. but move 25? why? whats to stop black from simply taking the rook with the queen?

Andrew, on 25... Qxe7?? White has 26. Qxd4+ Kb8 27. Qb6+ and after 27... Bb7 white mates with 28. Nc6+ Ka8 29. Qa7#.  After 27... Qb7 the immediate 28. Nc6 mates.

I have a soft spot for the "octopus knight" game (Karpov vs. Kasparov, 16th game World Championship match 1985). Category? Creative strategic idea.

http://www.chess.com/article/view/the-octopus-knight

http://www.chessgames.com/perl/chessgame?gid=1067175

Is Kasparov reported to have said which he thinks was his best game?

I am personally very fond of that game where he sacrifices the exchange in return for a stranglehold on the centre light squares, but that's mainly because I haven't seen many of Kasparov's games.

Game 16 versus Karpov from the second WC match :)

Seriously!

Bobby Fisher claims that game was prearranged, the fix was on.

Fischer was as mad as a bag of cats.

I kind of liked the game where Kasparov had to play the entire world. It was interesting to watch as the game progressed.

Yeah, this move is totally understandable.  I mean at first I thought it was crazy, but 10 seconds later when I saw all the way to 37.Rd7 I realized Kasparov had made the right choice [/sarcasm]

I still hope his greatest game is yet to be played!

He's younger than others who turned in world class performances - like Steinitz, Lasker, Botvinnik, Smyslov, Korchnoi, and even than Tal in some great performances.

Kasparov only retired because his wrenching the "real" title away from FIDE backfired when he lost to Kramnik and it became clear he would never get a rematch.  He could still come back and compete at the highest level.  Remember that even Carlsen has still not equaled Gazza's peak rating.