The Monte Carlo simulation method is used to study the structure and phase transitions in adsorbed films formed on the (100) plane of the model face-centered cubic crystals characterized by the different corrugation of the surface potential. The systems consisting of the adsorbate atoms that tend to form the c(2 x 2) registered phase are studied. It is shown that the actual structure of the dense monolayer films depends on the corrugation of the surface potential and on the density of the adsorbed layer and the temperature. The mechanism of melting transition in submonolayer, monolayer, and bilayer films is discussed. In particular, it is demonstrated that the submonolayer (incommensurate and registered) films retain monolayer character upon melting, whereas melting of a dense (incommensurate) two-dimensional solid is accompanied by the promotion of the second layer. The phase diagrams for a series of systems are determined. It is shown that the location of the critical point for the first-layer condensation is affected considerably by the surface corrugation. In the second layer formed on weakly corrugated surfaces and built on top of the dense incommensurate first layer, the effects due to the surface potential corrugation seem to be negligible. One observes the strong influence of the first-layer roughness (induced by the surface potential corrugation) on the critical temperature of the second-layer condensation only in the strongly corrugated surfaces.