As a basis for the interpretation of data gathered by LOPES and other experiments, we have carried out Monte Carlo simulations of geosynchrotron radio emission from cosmic ray air showers. The simulations, having been verified carefully with analytical calculations, reveal a wealth of information on the characteristics of the radio signal and their dependence on specific air shower parameters. In this article, we review the spatial characteristics of the radio emission, its predicted frequency spectrum and its dependence on important air shower parameters such as the shower zenith angle, the primary particle energy and the depth of the shower maximum, which can in turn be related to the nature of the primary particle.