We Jews [specifically in Israel, IIRC] also pray and fast for rain in times of extreme drought. This happened three years in a row, when I was a child, but, thank G-d, only once since then. There is half a Tractate of the Talmud/Mishna dedicated to this topic, defining under what conditions this is done, and how. The "how" requirements get stricter as the drought progresses through the rainy season.