This paper presents the hypothesis that intrinsic, apparently goal-free, motor-centric activity is a fundamental and necessary component of cognitive development in truly autonomous intelligent agents, both human and artificial. We argue that such intrinsic activity is the source of both early motor babbling behaviour and the much more complex play behaviours of older children (and even adults). We also show how babbling/play may be implemented as a form of unsupervised shaping. These ideas are a consequence of our experience of building models in developmental robotics, from which the necessity to recognise and incorporate intrinsic activity in artificial cognitive agents became imperative. We summarise some of the findings from our experiments in order to illustrate the basis of these ideas.