I went camping in Big Basin and it poured cats and dogs for 3 days straight, with absolutely no letting up. Even though it wasn't ideal, I gained thicker skin and learned a few tips and tricks.
Using tarps and canopies, we set up a tent city, and spent most of our time living outdoors. It took some effort, but we started a bonfire and used that to warm ourselves. The heat creates a little pocket of dryness around it.
I also took rain walks, which gave me a different perspective on hiking. You do have to be careful of flash floods, slippery trails, and hypothermia.
Reading books, playing cards, and socializing are all great ways to enjoy your time camping in the rain.