For me one of the best times to shoot street is when it is raining, granted there needs to be no wind otherwise it becomes a bit tricky trying to hold onto your umbrella with one hand while you do your best to focus, compose and shoot with the other hand.
But once you master I find the photos to be more interesting with regards to subject and lighting. Also it seems that people tend to care far less about you taking their photo when it is pouring down with rain as they are so preoccupied with trying to stay dry.