Versatile cleaning composition that has tremendous cleaning power, yet is compatible with many surfaces. For example, the cleaning composition easily cleans oil, grease, tar, and rubber from soiled surfaces, but does not damage metals, vehicle paints, concrete, plastics such as polycarbonate, MYLAR polyester and silicone sealants, wood, ceramic, and the like. The cleaning composition includes an oil solubilizing amount of a degreaser, a rubber solubilizing amount of a rubber solvent, and a polar, organic diluent. In preferred embodiments, the degreaser comprises a glycol ether, the rubber solvent comprises an nonaromatic naphtha, and the diluent comprises an alcohol.