The “Scenario Machine” (a computer code designed for studies of the evolution of close binaries) was used to carry out a population synthesis for a wide range of merging astrophysical objects: main-sequence stars with main-sequence stars; white dwarfs with white dwarfs, neutron stars, and black holes; neutron stars with neutron stars and black holes; and black holes with black holes. We calculate the rates of such events, and plot the mass distributions for merging white dwarfs and main-sequence stars. It is shown that Type Ia supernovae can be used as standard candles only after approximately one billion years of evolution of galaxies. In the course of this evolution, the average energy of Type Ia supernovae should decrease by roughly 10%; the maximum and minimum energies of Type Ia supernovae may differ by no less than by a factor of 1.5. This circumstance must be taken into account at estimating the parameters of the Universe expansion acceleration. According to theoretical estimates, the most massive—as a rule, magnetic—white dwarfs probably originate from mergers of white dwarfs of lower mass. At least some magnetic Ap and Bp stars may form in mergers of low-mass main-sequence stars (M ≲ 1.5 M _⊙) with convective envelopes.