The force between two inert, planar surfaces in a liquid is discussed, focusing on the effect of the reduction in the fluid density between the surfaces. We use a density functional treatment of the fluid, the results of which are verified by comparison with grand canonical Monte Carlo simulations. Our calculations reveal the existence of an attractive force between the surfaces, which at short and intermediate separations is substantially stronger than that expected from the conventional Hamaker or Lifshitz theories. The source of the extra attraction is the interstitial density depression that results from the requirement of chemical equilibrium between the bulk and the confined fluid at all separations. Given inverse sixth power attractions between fluid molecules, the force between the inert surfaces asymptotically decays as the inverse third power of the separation. However, at short separations it displays a qualitatively different behavior. We also find that the attraction increases with temperature, at constant pressure, and decreases with increasing pressure, at constant temperature, contrary to standard Hamaker theory. These results should lead to a more cautious interpretation of some parameters obtained from fitting experimental surface force curves to, for example, the DLVO expression. Furthermore, in discussions of the molecular mechanism of the hydrophobic attraction, the focus is almost invariably on the short-range directional hydrogen bond, or electrostatic, forces. Our calculations suggest that the density depression mechanism could be as relevant as orientational order.