The stability of water droplets on striped surfaces exposing regions of different wettability is studied experimentally, numerically, and based on a scaling model. Different values of the stripe widths and different contact angle contrasts between the hydrophilic and hydrophobic stripes are considered. The boundary between the contact angle contrasts leaving the droplets intact and those leading to droplet breakup is computed numerically. The minimum contrast for which breakup occurs increases with increasing hydrophobic contact angle. The existence of an unstable and a stable regime is confirmed experimentally. In the unstable regime, when approching droplet breakup, a configuration with two liquid fingers on the hydrophilic stripes connected by a capillary bridge on the hydrophobic stripe is found. For decreasing volumes, the width of this capillary bridge decreases until a critical value is reached at which the droplet breaks up. The critical width depends on the ratio of the hydrophilic and the hydrophobic stripe width. A simple scaling model is presented with which the critical width can be predicted. According to the model, the droplet becomes unstable when the increasing Laplace pressure inside the bridge can no longer be balanced by the pressure inside the liquid fingers on the hydrophilic stripes.