This paper discusses the physical and mathematical foundations and possible applications of the intensity correlation method for spatial three-dimensional (3-D) positional detection (finding the 3-D spatial position) of distant γ-ray or neutrino sources in real time or after a set of registered events. This method is based on the correlation of intensities of event sequences measured by several spaced-apart distant detectors. A specific consideration is made of the possibility of using a correlation intensities method for the analysis of the processes within a nuclear reactor, for the search of the hypothetical intra-terrestrial georeactor (planetocentric nuclear fission reactors), for the optimization of the method of single-photon-emission-computed tomography in medicine, and for other applications. The conditions of successful applications of the intensity correlation method for these systems are determined. The main problem with this method is connected to a relatively low count rate of registered neutrino events.