We investigate pattern formation in the immiscible displacement of foam from a confining geometry. The dominant length scales with the driving pressure gradient as for a Newtonian fluid, but depends surprisingly on the ratio of plate separation to bubble diameter. The pattern morphology exhibits a transition from a jagged, presumably elastic, character to a smooth, viscous character as the shear strain rate rises far above the natural internal relaxation time scale of the foam. These features may result from the two-dimensional nature of the flows and the unusual rheology of foams.