I read to them all the time--it's our favorite thing to do. We read picture books and chapter books and encyclopedias and I even read recipes on the rare occasion I can handle the mess and stress of cooking with them.
I sometimes give them a starter idea, like this morning when I handed them a cardboard tube full of plastic dinosaurs and suggested they create a prehistoric dino-land in the sandbox (and later have a dino-wash with soap and scrub brushes before the dinos are allowed back in the house), and I often set them up with supplies so that they can be creative (like the cardboard spaceship/doghouse that is on our front porch, complete with pink tissue paper and sparkly alphabet stickers), and OCCASIONALLY I may get talked into playing a board game or even a game of catch in the backyard.
But overall, I trust they will keep themselves occupied. I even ignore them. And...to tell the truth, I think it's good for them. They know that I am always available for a hug or a kiss. They know that I am frequently available for a "Wow! That sounds awesome!" and they know that sometimes I'm even available for a "Come see, Mama!" They are always supervised, albeit sometimes through the window or even via the baby monitor that is still on in the hallway outside their bedroom.
But really, I remember when that grandma who devotes every moment to her little Jabber and her little Monkey told me to "go play outside" as she handed me a cup of Kool-Aid and locked the door behind me. (It's hyperbole, Mom...no, you didn't really lock the door. At least, not when it was below zero. Not when there was lightning. Much.) I remember playing board games with myself. (I even played Stratego against myself, which, if you know the object of Stratego, is pretty lame.) I read books, drew pictures, played elaborate games with my stuffed animals and My Little Ponies and taught myself to play guitar and basically turned out okay. And I was all alone for the nine years I waited for my parents to get around to giving me a sibling. My kids are so lucky--they have a built in
So yeah, I think they sometimes start acting crazy because they're tired of hearing the tapping of my fingers on the keys and tired of waiting for me "to just finish this scene". And sometimes I really would probably have more fun if I put down my paintbrush and helped them dig a dinosaur bog. But overall, I'm happy with the way they can occupy themselves. And when I see Jabber ride by on his bicycle, with his superhero mask and his tool belt full of mysterious objects, funny voices emanating from his constantly flapping mouth...or when I see Monkey, stubbornly wearing his fireman boots and holding "a lava bomb" as he sits on top of his "rowing crusher"--I think about how the freedom to occupy themselves might help them cope with life better than if I'm constantly guiding them or providing them with activities.
I admit, there are ways to have the best of both worlds, ways that I periodically flirt with but ultimately find myself too adult-busy for. A long time ago when I read the book Playful Parenting, I was really impressed with the free play time, where parents are told to play with the kids but to let the kids have the reins. I further admit that this is hard for me. I know that my kids love it when we do some of the things I read about in this book, especially playing with puppets or dolls or whatever to work through problems, teach lessons, build empathy. So I try some of that, telling stories using some puppets we have--stories about a big brother and a little brother who don't always get along.
But more often than not, I hand them a cup of Kool-Aid and send them out the door.

And here's my youngest son Monkey, who at sixteen months, is completely fearless.