Since we started producing nuclear power in 1960, how common are large nuclear accidents (those that resulted in the major release of radioactive material into the environment)?

Very, very rare. Uranium used in power plants is typically only 3% U-235 (the explosive stuff), while bomb-grade uranium is nearly pure U-235. Simply, the concentration of U-235 in reactor-grade uranium is too small to start a chain reaction and detonate like a bomb.