Fortune Teller: Immensely popular with the elementary crowd; kids love the idea of telling each others fates, and they can get very creative when making up fortunes. Don't worry about using black paper and gel pens like the directions suggest. That makes the fortune teller extra cool looking but isn't necessary.
Balloon/Water Bomb: These balloons are a blast to blow up. It's fun to see how long you can keep hitting it up in the air.
Simple Box: Boxes can store all sorts of things. One thing you could do is have your child make one to hold a gift. To make a top, fold another box using paper that is a few centimeters larger.
Jumping Frog: These jumping frogs are fun to play with! I recommend using card stock as paper to get a better jump.
Money Origami: How cool is this?!? You can make a bow-tie, a shirt, or try one of the more challenging folds. Your child will love it because, not only does it look neat, but it's made out of money. Try paying for something with a lucky star and see what happens!
Paper Airplane: Though not strictly origami, paper airplane folding and flying can waste hours on a rainy day. I give my kids a stop watch for them to see how long they can keep their plane in the air. Who can beat the record? You can also try these other styles -- Airplane 2, Airplane 3