The spreading and rebound patterns of low-viscous droplets upon impacting spherical solid surfaces are investigated numerically. The studied cases consider a droplet impinging onto hydrophobic and superhydrophobic surfaces with various parameters varied throughout the study, and their effects on the postimpingement behavior are discussed. These parameters include impact Weber number (through varying the surface tension and impingement velocity), the size ratio of the droplet to the solid surface, and the surface contact angle. According to the findings, the maximum spreading diameter increases with the impact velocity, with an increase of the sphere diameter, with a lower surface wettability, and with a lower surface tension. Typical outcomes of the impact include (1) complete rebound, (2) splash, and (3) a final deposition stage after a series of spreading and recoiling phases. Finally, a novel, practical model is proposed, which can reasonably predict the maximum deformation of low Reynolds number impact of droplets onto hydrophobic or superhydrophobic spherical solid surfaces.