A self-propelled lawn mower including at least one cutting blade and at least first and second rear drive wheels. Hydro pumps are provided for controlling the drive wheels. Optionally, a grass collection system may be mounted on the mower, with much of the system being located laterally rearward of the rear drive wheels so that the center of gravity of the mower is shifted rearwardly. In order to compensate for such a center of gravity shift, the respective positions of the rear drive wheels are adjustable. In certain example embodiments of this invention, the lateral position of the rear drive wheels may be selectively adjusted as desired by the operator (e.g., to move the center of gravity of the mower forward relative to the rear drive wheels in order to compensate for the added rear-heavy weight of the grass collection system).