We introduce a new lattice-based Monte Carlo model of polymer dynamics in which the polymer chain topology can be altered without perturbing any static properties or the local segment mobility. Chain entanglements can then simply be switched "on" and "off," and their effects on global dynamics can be clearly isolated. Two sets of simulations have been conducted for bulk polymer melts. In the first set chain crossing is rigorously forbidden, but in the second set the polymer chains are allowed to cross through each other. When the chains are not allowed to cross, the self-diffusion coefficient exhibits the classic signature of the crossover from unentangled to entangled dynamics. For short chains, D similar to N-1, while for long chains, D similar to N-2, where D is the diffusion coefficient and N is the number of polymer segments. Furthermore, the longest noncrossing chains show a clear preference for anisotropic motion along their own contours-they appear to move by reptation. When the chains are allowed to cross, however, D similar to N-1 at all chain lengths, characteristic of unentangled dynamics. No crossover is indicated in this case, and no signs of reptation are present. Since the structure and local mobility are nearly identical in the two cases, the dynamical differences are due only to the chain topology through the crossing condition. We discuss how the results illustrate the role of entanglements in bulk polymers and how the model may be used in the future as a tool to examine entanglement effects in adsorbed layers and confined polymer fluids.