We carry out extensive molecular dynamics (MD) simulations of translation and rotation of spheroids in the suspension of spheres, for a wide range of values of the aspect ratio, kappa ranging from the extreme limits of long rodlike molecules to the disc-shaped ones. While diffusion is anisotropic in short times (compared to the orientational correlation time), it is isotropic in the very long time and the ratio of the two components of short time translational diffusion (D-parallel to and D-perpendicular to, where parallel to and perpendicular to refer to the motion parallel and perpendicular to the major axis) scales with the aspect ratio kappa over a large range of kappa. For thin discs, the preferred mode of motion is in the plane of the disc. The oblates show a very long-time orientational correlation which is reflected by the slow decay of its time correlation function. The correlation time becomes progressively longer and finally diverges as the spherical limit is approached. This is expected because the angular momentum is conserved in the limit of fully spherical molecules (kappa =1). For both prolates and oblates, the crossover from the anisotropic to the isotropic motion is found to correlate with the orientational correlation time of the spheroid.