We show, using numerical simulations, that a rich variety of novel colloidal crystalline states are realized on square and triangular two-dimensional periodic substrates which can be experimentally created using crossed-laser arrays. When there are more colloids than potential substrate minima, multiple colloids are trapped at each substrate minima and act as a single particle with a rotational degree of freedom, giving rise to a new type of orientational order. We call these states colloidal molecular crystals. A two-step melting can also occur in which individual colloidal molecules initially rotate, destroying the overall orientational order, followed by the onset of interwell colloidal hopping.