Transport properties of five room-temperature ionic liquids based on the 1-butyl-3-methylimidazolium cation with any of the following anions, [PF6](-), [BF4](-), [CF3SO3](-), [NTf2](-), and [NO3](-), were determined from classical molecular dynamics simulations. The force field employed fractional ion charges whose magnitude were determined using condensed phase quantum calculations. Integrals of appropriate equilibrium time correlation functions within the GreenKubo approach were employed to predict shear viscosity and electrical conductivity of these liquids. Computed shear viscosity values reproduce experimental data with remarkable accuracy. Electrical conductivity calculated for [BMIM][PF6] and [BMIM][BF4] showed impressive agreement with experiment while for [BMIM][CF3SO3] and [BMIM][NTf2] the agreement is fair. The current approach shows considerable promise in the prediction of collective transport quantities of room temperature ionic liquids from molecular simulations.