njchess: A famous game from two would be champions. As for the game and where Fischer went wrong...
7. ... Be7 a passive move that leads to early castling allowing White too much time to get his attack going. Generally, b5 is played, though Nbd7 and Nc6 (Scheveningen) are viable. 8. f4 is preferred over g4, which is equally sound, probably because Fischer preferred to castle short in this position.
8. ... 0-0 is consistent with the previous move. 9. Qf3 (9. f5 exf5 10. Nxf5 Bxf5 11. exf5 Qb6 12. Qf3 d5 ) is White's best move. 9. ... Qc7 (9. ... Nc6 10. Be3 Qc7 11. g4! Re8 12. g5 Nxd4 13. Bxd4 Nd7 `14. 0-0-0 b5 15. g6! hxg6 16. h4 ) is Black's best reply.
10. 0-0? is a critical slip. Tal's previous moves might have given Fischer the belief that he had the time to play this move, but he does not. f5 or even Be3 are better plays. 10. f5 e5 11. Nde2 b5 12. a3 Bb7 13. g4 Nbd7 14. g5 Nxe4 15. Nd5 Nxg5 or, 10. f5 Nc6 11. Be3 Nxd4 12. Bxd4 e5 (12. ... b5 13. a3 exf5 14. exf5 Bb7 15. Qh3 Nd7 16. 0-0-0 ) 13. Be3 b5 14. a3 Bb7 15. 0-0 Bc6 (15. ... Rac8!?) 16. Bg5 Nxe4?! 17. Bxe7 Nf6 18. Nd5! Nx5 19. Bxf8 Nf4 20. Qg4 With 10. ... b5, Tal correctly launches queenside counter play.
Fischer plays 11. f5?, underestimating the impact of 11. ... b4!. Not only does it force Na4 (a less than ideal square for the knight in this position), but in combination with 12. ... e4, it allows Tal to 1) undermine White's center, 2) effectively control the a1-h8 diagonal and 3) bring White's attack to a standstill. This is the turning point in the game. Objectively, 11. a3 lets Black achieve full equality after 11. ... Bb7, but nothing more. 11. e5!? leads to an extremely double-edged position slightly favoring Black.
While Fischer spends time maneuvering his knight back into play, Tal simply develops. 13. Ne2 Bb7 14. Ng3 Nbd7. 15. Be3 is normally the correct move in this type of position. However, given White's lack of counter play, I'm surprised Fischer did not play Bg5 or even c3 to try to get his knight back into play. With 15. ... Bc6 and 16. ... Qb7, Tal correctly attacks White's weak hanging pawn. Note that Fischer has almost zero counter play at this point. 16. Bf2 followed by 17. Rfe1 is preferred over c3 as means of defending e4.
Tal prefers the immediate 17. ... d5 over Rac8. 18. exd5 Nxd5 19. Ne4 Nf4 yields Tal a small but tangible advantage. At this point, we have reached a critical juncture. Black is threatening Nf6 thereby attacking the knight on e4, as well as the queen on f3 and the g2 pawn. The only way to counter that attack is for White to play Bc2.
Fischer chooses the aggressive and not altogether sound 20. c4?!. While the pawn seems to be left hanging in the breeze, it is in fact quite safe after Bc2 and b3. Moreover, it controls d5 and b5, and with his knights controlling c5, forms a blockade of sorts. The obvious concession is that his bishop is relegated to a defensive position, but more importantly, Fischer's options for counterplay dwindle to nothing. Objectively, c3 might have been better, though I doubt it.
While Fischer's 20th move is questionable, Tal's 20. ... g6 is not. Tal correctly seizes on the idea that opening the king side will benefit him more since he already has so much material aimed that way. 21. fxg6 is not much better than 21. f6 Nxf6 22. Nac5 Qc7 23. Nxf6+ Bxf6 24. Qg3 Bxg2
At this point, the knight on f4, Tal's control of the h1-a8 diagonal and White's open kingside are just too much for Fischer.