If you have children with you, you will have no worries about keeping yourself busy, you'll be plenty busy. If the weather is nice, your kids might enjoy games like:
- Throw Rocks in the Water
- Run Around As Fast As You Can
- See If You Can Throw A Prized Toy Into A Tree And Get It Stuck There
- Find A Stick and then Fight Over Whose Stick It Is
My kids also liked Get Firewood and Purify Water (with a hand pump device) because kids like to help. In crummy weather, story books in the tent, and perhaps colouring (with coloured pencils, they travel better than crayons) are old standbys. The adults, of course, are busy keeping the kids safe and generally watching for trouble. Not to mention cooking, cleaning, and straightening up things that got messy over the day, like putting things back where they belong, hanging up wet things, and bringing dry things into the tent so they stay dry. It's also possible you might be talked into wading into the deep water to retrieve all the rocks they threw in, so they can throw them in again.
No kids? I guess in this case it is theoretically possible to be bored, though it hasn't happened to me on childless trips (they grow up eventually and you can go out without them.) Try:
- read a book
- lie on a warm rock and let the sun shine on you
- write something in your journal
- meditate, stretch, do yoga
- get firewood, purify water, make dinner, do the dishes, ...
- talk to the person you are with
- learn how to skip stones
- carve a little something out of wood
- sit around the campfire and watch the flames
- daydream a little and try to plan out your long term goals and wishes (the peace and quiet of nature makes this easier to do)
- play cards in the tent if the weather is bad
- look at the maps and plan another trip to another part of the place you are in
- trade books with the others if you read all you brought
On a completely stay-put day you can also practice tipping your boat, swimming in your PFD, and other "emergency" drills when your possessions are all safe and dry on the shore. If you are not boating, you could practice starting a fire without matches, learn to tie various knots (bring a sheet or two of instructions), and generally experiment with stuff to make you better at the camping you do.
I typically bring my books home unopened, but I always take at least one just in case.