More wonderful materials from Azure Magazine to deal with water run-off- Geo-cells. These are open-grid plastic systems that are filled with gravel or grassy turf. They support the weight of vehicles but let the water run through easily.
Grasspave from the appropriately names Invisible Structures, is a plastic mat that is rolled out onto a prepared bed, filled with appropriate landscaping, and you let it grow. Doesn't look like it, but it can hold up firetrucks. "Grasspave2 porous paving allows you to park, drive, walk, ride, or lounge on a beautiful grass surface. It performs the functions of asphalt or concrete pavement, but with the aesthetics of a lawn – all while enhancing the environment." They also make Gravelpave that can be used for commercial parking lots.