Using a two-dimensional Scheutjens and Fleer self-consistent field calculation, we determine the equilibrium morphology of thin films of symmetric AB diblock copolymers confined between hard, smooth plates. A lamellar phase is established with the stripes either perpendicular or parallel to the walls. With neutral walls, the perpendicular orientation is stabilized by the nematic ordering of the monomers, which arises from the orientational constraint imposed by the walls. When the substrates are composed of pure A monomer (thus repulsive to B), there are transitions from strained parallel conformations, which wet the substrates with A polymer, to distorted perpendicular configurations as the film thickness is varied. It is possible that the removal of one of the walls (the usual experimental scenario of thin films spun cast onto a substrate) can still lead to spontaneous and robust pattern formation on the scale of tens of nanometers.