Plasma applications of computational techniques based on cellular automata are inhibited by the long-range nature of electromagnetic forces. One of the most promising features of cellular automata methods has been the parallelism that becomes possible because of the local nature of the interactions, leading to the absence of Poisson equations to be solved in fluid simulations. Because it is in the nature of a plasma that volume forces originate with distant charges and currents, finding plasma cellular automata becomes largely a search for tricks to circumvent this nonlocality of the forces. We describe automata for two situations where this appears possible: two-dimensional magnetohydrodynamics and the one-dimensional electrostatic Vlasov-Poisson system. Insufficient computational experience has accumulated for either system to argue that it is a serious alternative to existing methods.