Knowledge of the ion motion in room temperature ionic liquids (RTILs) is critical for their applications in a number of fields, from lithium batteries to dye-sensitized solar cells. Experiments on a limited number of RTILs have shown that on macroscopic time scales the ions typically undergo conventional, Gaussian diffusion. On shorter time scales, however, non-Gaussian behavior has been observed, similar to supercooled fluids, concentrated colloidal suspensions, and more complex systems. Here we characterize the diffusive motion of ionic liquids based on the N-butyl-N-methylpyrrolidinium (PYR14) cation and bis(trifluoro methanesulfonyl)imide (TFSI) or bis(fluorosulfonyl)imide (FSI) anions. A combination of pulsed gradient spin-echo (PGSE) NMR experiments and molecular dynamics (MD) simulations demonstrates a crossover from subdiffusive behavior to conventional Gaussian diffusion at ∼10 ns. The deconvolution of molecular displacements into a continuous spectrum of diffusivities shows that the short-time behavior is related to the effects of molecular caging. For PYR14FSI, we identify the change of short-range ion-counterion associations as one possible mechanism triggering long-range displacements.