In New York we do a few things.
Spider boxes, stage boxes and lunch pails can all be put up on apple boxes or what we call swamp boxes to keep metal up and off the ground.
A piece of rubber matt over the whole thing usually keeps things dry. It's not great idea to use black garbage bags as they look like garbage bags and I have seen stage boxes crushed by a truck that rolls over it.
We use cam lock on our cable runs that are supposedly water proof so we don't usually cover those connections but I don't like them in ponding water if there is any or in the street where a truck can run them over.
The lights: If it's going to rain I'll look for a shelter for stage boxes and HMI ballasts along a building or under an awning or something. If no shelter is available I like to cover ballasts with rubber matte but is such a way the ballast can breath. If they over heat your lights will go out. Many guys will use what we call cellotex. It is a screen with some sort of clear fiberglass/plastic material on it. We use it to cover lighting heads or ballasts while it is raining. It must be put on is such a way that it covers enough of the barn doors where the lens is cover from above.
If it is really raining hard, you can use UV filter or Heat shield to cover the lens.
If you are shooting on the beach you may want to cover HMI connectors from sand or mud.