One popular childhood project for many of us was building a crystal radio, but those radios still required a battery to run. MAKE Projects has come up with a newer version of this crystal radio that you can build with a bottle and no power source at all.
The project itself is very detailed, but like most crystal radio builds it isn't too difficult to complete. You'll need a variety of materials and quite a bit of wire in addition to a glass bottle to make it work. The upside to this project is not so much that you'll have an inexpensive, power-free AM radio for a few dollars (as you can likely buy one at a thrift store for less than the cost of these materials), but that this is a great DIY starter project to help you learn how to build your own technology.
If you've been looking to get into more complex electronics-building but have been a little intimidated, this is a great place to start. Additionally, it's a really fun project to do with your kids if you want to teach them these basics skills. MAKE also notes that AM broadcasting is slowly going away, meaning there's a limited time to partake in a project like this before it's forgotten entirely. Whether you want to build it out of nostalgia, to learn some new skills, or to pass skills on to the next generation, this is a fun and inexpensive way to do it.
For project details, hit up MAKE for the full how-to and parts list.
Bottle Radio [MAKE Projects]