When my niece lived with me she always wanted to help me build or work in computers. Ever since she moved almost every time she'd visit she would ask if we could fix my computer, so I thought getting a Pi and making a custom case together would be a cool day project while she visited. She loved it, picking out the materials, drilling, filing, securing the nuts and bolts, and the end result of playing Minecraft. it was a joy to see how much she enjoys computers.
She's 7 and I want to get her a Pi for her at her house and I want to find some projects that she will enjoy aside from the listed ones. Anything is a good idea in this case. If you have kids or children that you use your pi with and have done a project I'd love to hear it, or if you've read about one that seemed like a good way to allow children to get their feet wet I'd be happy to hear! The projects don't need to be super creative or indepth, a simple dot matrix emoticon display would do, however I'm not limited to a budget or anything so an arcade machine, robot, bird feeder cam, bedroom alarm system, etc would also be cool!