Michael B's answer is pretty good, except for a few things:
1) The French Revolution did try to do away with religion, but to say France was "not influenced" by not really correct.
2) the socialist revolutions of the U.S.S.R. and other countries were officially atheist, but again, to say they "weren't influenced" by religion is not totally correct.
3) Mexico has never had a "communist revolution." At least one of the leaders of the revolution that began in 1910 (Emiliano Zapata) was an anarchist. And it's true that churches were closed for a few years in the 1920s, but this was a decision of the Catholic Church (as a reaction to some anti-Church policies of the government).
Going back in history, China owes much of its history to Confucianism, which is a philosophy, not a religion. Buddhism and other religions have also influenced China, but Confucianism stands out head and shoulders above the rest.