Variational calculations are presented of the ground exciton state in quantum wells. For the GaAs-GaAlAs system, the results obtained from a trial wave function not separable in spatial coordinates are shown to be valid throughout the entire well-thickness range, corresponding in the thin and thick limits to two- and three-dimensional situations, respectively. For the InAs-GaSb system, in which electrons and holes are present in spatially separated regions, the exciton binding is substantially reduced. In the limit of thin wells, the binding energy is only about one-fourth of the two-dimensional value. © 1982 The American Physical Society.