Amateur radio aka ham radio is a hobby practiced by over 6 million people worldwide. It's a service set up by individual governments (the FCC in the US) but is largely run by hams themselves. The primary advantage of being a licensed radio amateur is the privilege of transmitting radio signals on certain frequencies. You can transmit around the world or even communicate with astronauts aboard the ISS or Space Shuttle.
You'd think that with the advent of texting, instant messaging, cell phones and sat phones, that amateur radio would fade into obscurity. The truth is that we hams are needed more than ever. Let's face it, whenever there's a disaster, the phone lines and web bog down to near-paralysis -- but the hams keep going, providing critical communication support during crises. (The body that handles emergency assistance in the US is called RACES.)
One of the coolest aspects of the amateur radio hobby, from the geekdad perspective, is that kids work with adults as equals. There isn't some special level of certification for children, it's all the same. So whether you're 7 or 107, as long as you can pass the test you can be a licensed ham. Even better, there are tons of opportunities out there for radio friendly kids. For instance, the American Radio Relay League Foundation offers scholarships for deserving kids. There is a radio merit badge for Boy Scouts, special kids-only ham radio clubs, as well as the opportunity to tinker with the geekkid's best friend, the radio controlled vehicle.
So how do you get started? First you must get licensed. Track down your local ham radio club and find out when they conduct exams. Then study up! One of the best printed resources for exam preparation is the ARRL Ham Radio License Manual: All You Need to Become an Amateur Radio Operator.