Transport properties of spherical and linear molecules modeled by the Kihara potential are studied by molecular dynamics simulations. Diffusion coefficients, shear viscosities, and thermal conductivities are calculated for a wide range of the fluid region and for several elongations. The corresponding individual and collective correlation functions are discussed along with angular velocity and reorientational correlation functions. Relaxation times and simple models relevant to orientational motion are also studied. The results obtained are discussed in a corresponding states framework, using previous Gibbs ensemble Monte Carlo data for the liquid-vapor equilibria of the models. In this way, the role of elongation can be studied. It is found that in most of the liquid region, the diffusion coefficient is weakly dependent on elongation. On the other hand, both viscosity and thermal conductivity are found to decrease with elongation. The dependence of transport coefficients on density and temperature is also discussed. On testing the Stokes-Einstein relation, it was observed that, unlike previous findings for hard spheres, stick boundary conditions perform just as good as slip boundary conditions for the Lennard-Jones fluid and the low-elongated Kihara fluid.