The electronic transport properties of graphene and suspended (intrinsic) graphene sheets are studied using an ensemble Monte Carlo (EMC) technique. The combined scattering mechanisms that are taken into account for both cases are nonpolar optic and acoustic phonons, ionized impurity, interface roughness, and surface polar phonon scatterings. The effect of screening is also considered in the ionized impurity and surface polar phonon scatterings of electrons. A rejection technique is used in EMC simulations to account for the occupancy of the final states. Velocity-field characteristics of graphene and suspended graphene sheets are obtained using various values of acoustic deformation potential constants. The variation of electron mobility of graphene is studied as a function of electron concentration and its variation as a function of temperature are investigated for the case of suspended graphene. For the former case, the mobility increases with electron concentration first and after a certain value of electron concentration it begins to decrease, while for the latter case the mobility decreases almost linearly with temperature. The mobility results from EMC simulations are compatible with the existing experimental studies for the unsuspended graphene case.