An electronic device may have a flexible housing formed from flexible fabric, flexible polymer, or other flexible materials. Cameras may be mounted on the housing. The housing may be bent into different configurations such as a configuration in which the housing has a convex surface facing an exterior region and a configuration in which the housing has a concave surface facing the exterior region. The cameras may have respective camera image capture directions. By reorienting the cameras by bending the housing, the cameras can be used to capture panoramic images or three-dimensional images.