An engineering risk assessment of the conditions for massive explosions of cryogenic liquid hydrogen-oxygen rockets during launch accidents is presented. The assessment is based on the analysis of the data of purposeful rupture experiments with liquid oxygen and hydrogen tanks and on an interpretation of these data via analytical semiquantitative estimates and numerical simulations of simplified models for the whole range of the physical phenomena governing the outcome of a propellant-tank breach. The following sequence of events is reconstructed: rupture of fuel tanks, escape of the fluids from the ruptured tanks, liquid film boiling, fragmentation of liquid flow, formation of aerosol oxygen and hydrogen clouds, mixing of the clouds, droplet evaporation, self-ignition of the aerosol clouds, and aerosol combustion. The power of the explosion is determined by a small fraction of the escaped cryogens that become well mixed within the aerosol cloud during the delay time between rupture and ignition. Several scenarios of cavitation-induced self-ignition of the cryogenic hydrogen/oxygen mixture are discussed. The explosion parameters in a particular accident are expected to be highly varied and unpredictable due to randomness of the processes of formation, mixing, and ignition of oxygen and hydrogen clouds. Under certain conditions rocket accidents may result in very strong explosions with blast pressures from a few atm up to 100 atm. The most dangerous situations and the foreseeable risks for space missions are uncovered.