If the chess world had to single out one game as the most studied, it’s Morphy vs. Allies, Paris opera house 1858.
http://www.chessgames.com/perl/chessgame?gid=1233404
Born in 1837, Paul Morphy was recognized as the first great chess genius. After he demonstrated that he could beat everyone in his hometown club in New Orleans, the First American Chess Congress was organized in 1857, partly to discover how the young Morphy would fare against the best players in the country. Morphy won that tournament handily, and then the only remaining question was whether he could beat the best players in Europe. So Morphy sailed over the Atlantic, and since he was a well-bred, polite young fellow with an incredible gift, the royals and chess officials in London and Paris loved him, taking him to all the best places.
The story goes that the Duke of Brunswick and Count Isouard de Vauvenargue took Morphy to the Paris opera to see The Barber of Seville, and shortly before the show began, the Duke pulled out a pocket set and asked for a game. Morphy said no, there isn’t time, and we’re out for a party, yo. But the Duke insisted, and Morphy said OK, let’s make it fast.
The 17-move gem goes down in history for its exceptional brilliance, and also because every move leading to the neat finish means something. One of the hallmarks of a great game of chess is that its moves can be tied together by positional logic — not only is Morphy-Allies bound by three or four discrete positional threads, each thread is instructive. A decent chess educator will probably make Morphy-Allies the first game that a promising student must memorize and understand, because its underlying lessons are the foundation for many time-tested principles.
The Kasparov-Deep Blue games were nothing special in terms of chess, but were historic in terms of chess software development.