It is part of information theory folklore that, while quantum theory prohibits the generic (or universal) cloning of states, such cloning is allowed by classical information theory. Indeed, many take the phenomenon of no-cloning to be one of the features that distinguishes quantum mechanics from classical mechanics. In this paper, we argue that pace conventional wisdom, in the case where one does not include a machine system, there is an analog of the no-cloning theorem for classical systems. However, upon adjoining a non-trivial machine system (or ancilla) one finds that, pace the quantum case, the obstruction to cloning disappears for pure states. We begin by discussing some conceptual points and category-theoretic generalities having to do with cloning, and proceed to discuss no-cloning in both the case of (non-statistical) classical mechanics and classical statistical mechanics.