The immortal game was very inaccurate despite having a beautiful finish, along with most of the romantic KGA games. My personal choice for greatest game is Morphy's opera game - Morphy's play is beyond reproach from start to finish and it is a perfect example of development and attack. Greatest is a matter of opinion - some games of Tal, Nezhmetdinov, or Kasparov have incredible ideas in them, but I view greatest as one side having perfect play.
Kasparov - Topalov, 1999. It's basically known as Kasparov's Immortal Game. It was a Pirc if I remember right.
Thriller, yes - 150 attack in the Pirc - that's the one with the R sac on d4, right?
When Roman D was in the mood he could produce some really nice tactics. This one has 2 nice "line blockage" type tactics, which to me makes it special. The crazy thing is that it could have had another one on move 30! (Be5 discovered check)
the best game i think anyone ever played is bobby fischer vs. donald byrne but i don't know if that is the greatest...