We always think that we want a clear bright day for photography. Well, maybe not. Whenever I see an overcast day for photography I smile. The sky is like a great big soft box making all the light even and beautiful. There are no nasty shadows or bright spots. Everything has great lighting. You may need to add some flash to give the photo some pop but this is not necessary. But still remember the sun is up there somewhere. Pay attention so your subject has the filtered sunlight on them. That means the sun is at your back.
Now how about rain? Some of the most amazing photos are taken in between rain drops when the street or grass is full of reflection. This can be particularly lovely at night with some city lights reflecting on a shiny street. Endless possibilities for creativity.