In the wave-optics numerical simulations of laser beam propagation in volume atmospheric turbulence, we observe irregular appearance of giant intensity spikes with amplitudes exceeding the diffraction-limited intensity value by a factor of ten or even more. The presence of giant spikes may explain the existing significant difference between the scintillation index theoretical prediction and the results obtained in numerical simulation and experimental measurements. The giant spikes' physics-based origin, probability of appearance, and impact on irradiance scintillation index are analyzed.