It depends on the camera.
I will use my Leica M4-P in light sprinkles. My Nikon F100 gets used in rain that I would not subject my M4-P to. I still use caution and keep if from getting soaked, though.
I have seen people wear "umbrella hats" at county fairs and outdoor sports events. They are basically an umbrella canopy around 18" in diameter (maybe a bit smaller) that is attached to a headband. I have often thought that one of these would be a great help in keeping the camera from getting drenched when photographing in the rain.
You would look like a total tool wearing one, but if it keeps the inside of your camera from suffering the same fate as the one in Ron's photos (above), it is well worth looking like a dork. Who cares what strangers think anyway?