A wide variety of approaches, ranging from Petri nets to systems of partial differential equations, have been used to model very specific aspects of cellular or biochemical functions. Here we describe how an agent-based or dynamic cellular automata (DCA) approach can be used as a very simple, yet very general method to model many different kinds of cellular or biochemical processes. Specifically, using simple pairwise interaction rules coupled with random object moves to simulate Brownian motion, we show how the DCA approach can be used to easily and accurately model diffusion, viscous drag, enzyme rate processes, metabolism (the Kreb's cycle), and complex genetic circuits (the repressilator). We also demonstrate how DCA approaches are able to accurately capture the stochasticity of many biological processes. The success and simplicity of this technique suggests that many other physical properties and significantly more complicated aspects of cellular behavior could be modeled using DCA methods. An easy-to-use, graphically-based computer program, called SimCell, was developed to perform the DCA simulations described here. It is available at http://wishart.biology.ualberta.ca/SimCell/.