In the interests of making chemistry more environmentally friendly, room-temperature ionic liquids are currently being investigated as alternative solvents in industry and academia. In this paper, we present molecular dynamics simulations of 1-buthyl-3 methylimidazolium hexafluorophosphate ([bmim][PF6]). We compute radial distribution functions, average density, and mean-square displacements for the individual ions. With this information, diffusion coefficients are calculated and conductivities are estimated using the Nernst-Einstein relation. The time history of the mean-square displacement of the ions appears to indicate that the system exhibits complex dynamics with at least two different time scales for diffusion. We model this behavior using a generalized Langevin approach. Results compare well with experimental data reported in the literature.