In this work, we have performed molecular dynamics (MD) simulations to compare the structural and dynamical properties of three ionic liquids (ILs), 1-ethyl-3-methyl-imidazolium tetrafluorborate ([EMI(+)][BF4(-)]), 1,1'-dimethyl-4,4'-bipyridinium bis(tetrafluorborate) ([VIO(2+)][BF4(-)]2), and 1,1'-dimethyl-4,4'-bipyridinium bis(trifluoromethylsulfonyl)imide (bistriflimide in short) ([VIO(2+)][Tf2N(-)]2), aiming to discover the influence of ion rigidity on the physical properties of ILs. [VIO(2+)] is more rigid than [EMI(+)], and [BF4(-)] is more rigid than [Tf2N(-)]. [VIO(2+)][BF4(-)]2 has an anion distribution different from the other two by the higher and sharper peaks in the cation-anion radial distribution functions, reflecting a close-packed local structure of anions around cations. [VIO(2+)][BF4(-)]2 and [VIO(2+)][Tf2N(-)]2 have similar dynamics much slower than [EMI(+)][BF4(-)], and [VIO(2+)][Tf2N(-)]2 shows a more isotropic molecular distribution than [VIO(2+)][BF4(-)]2 and [EMI(+)][BF4(-)]. Additionally, we have simulated two modified viologen-based ILs to reinforce our interpretations. We conclude from the above simulation results that the rigidity of anions influences the alignment of cations and that the rigidity of cations shows a large obstacle to their rotational capacity. Moreover, we have observed a slower diffusion of [VIO(2+)][BF4(-)]2 due to the electrostatic correlations, which stabilizes the ion-cage effect.