"The rain has stopped." is the most common usage. However, you can say "The rains have stopped." when you are referring to an ongoing rainy season or monsoon. The rain has stopped. = There was a single rain storm that came through. The rains have stopped. = There were a series of rain storms. All of them have stopped. But we would more commonly say: The rainy season has stopped.

The rain has stopped is the correct sentence. Although the word "rain" represents a plural idea, it is a singular noun. Hope this helps :)