The Stokes-Einstein relation, relating the self-diffusion coefficient D to the shear viscosity eta (D = k(B)T/2 pi eta sigma) , is tested for two- and three-dimensional fluids. The influence of attractive potential and temperature on the validity of the Stokes-Einstein relation by employing square-well potential is analyzed. A breakdown of the Stokes-Einstein relation is observed at low temperatures for three-dimensional fluid by using the Nigra and Evans(11) model and with that obtained from the velocity autocorrelation function(10) and for two-dimensional fluids by using the Garcia-Rojo et al.(12) model for hard discs.