In simplified models of neocortical circuits, inhibition is either modeled in a feedforward manner or through mutual inhibitory interactions that provide for competition between neuronal populations. By contrast, recent work has suggested a critical role for recurrent inhibition as a negative feedback element that stabilizes otherwise unstable recurrent excitation. Here, we show how models based upon a motif of recurrently connected 'E-I' pairs of excitatory and inhibitory units can be used to describe experimental observations in sensory and memory networks. In a sensory network model of binocular rivalry, a model based on competing E-I motifs captures psychophysical observations about how incongruous images presented to the two eyes compete. In a model of cortical working memory, an architecturally similar model with modified synaptic time constants can mathematically accumulate signals into a working memory buffer in a manner that is robust to the abrupt removal of cells. These results suggest the inhibition-stabilized EI motif as a fundamental building block for models of a wide array of neocortical dynamics.