Motion processing in visual systems is supported by various subcortical and cortical microcircuits. However, all motion processing requires a basic capacity to integrate and combine information over time, as may be true for all microcircuits that support perceptual and cognitive functions. In the present study, a generic microcircuit model is presented that self-tunes its recurrent spiking dynamics to its critical branching point. The model is shown to have generic memory capacity that can be tapped for the purpose of visual motion processing. These results suggest that critical branching neural networks may provide general bases for spiking models of motion processing and other perceptual and cognitive functions.