Key to getting a good Russian character in a movie is finding and actor who is willing to go to Russia and try to understand what they're about to get a true sense of what they're like. Because in reality they are quite different then what most "outsiders" imagine them to be like. This is quite difficult to get an actor to cast aside his assumptions, learn a language, and deal with a lot of foreign people.
A successful example of this would be Mickey Rourke for Iron Man 2. Crappy accent, maybe shallow dialogue, but he "got" the essence of the Russian mentality, at least of a certain type of Russian.
Capturing the essence of a chess master from the Soviet Union would probably be very difficult to do correctly at least from a foreigners perspective.
Spassky was only 35 when Fischer challenged him for the title. Most of the actors suggested here are too old except maybe Daniel Craig. I'm thinking Michael Fassbender or possibly Christian Bale.