This is a good all weather cover that I've used:
weathershield HD
Light weight, but good water protection and breathable.
If I had to park a car outside, I would use some kind of cover. The sun and weather is destructive to the paint and interior over time, a good cover can keep the car looking new for years (decades, even!) where otherwise it would get faded.
As far as rain, if it were already raining, I would leave the cover off. Maybe throw something over the engine lid. But if you have the cover on and it starts raining, I'd leave it on.