It is very difficult for me to say only a few words about Ham radio. Ham radio is perhaps the most vibrant form of shortwave communication left. Emergency communications, conversations between friends and family in distant countries, and reports from yachts far at sea are some of things you can hear on the ham bands. In addition, hundreds of thousands of hams (myself among them) still use Morse code, keeping this art alive now that ships and the military have abandoned it. If you hear Morse code on shortwave these days, odds are it is a ham (or, every now and then, a spy).
In fact, until recently the FCC required amateurs to demonstrate the ability to receive Morse code at fifteen words per minute before granting them voice priviliges on the shortwave bands. Now, however, prospective hams are only required to demonstrate an ability to receive code at five words per minute (and pass a written theory exam or two). At five words per minute, it is only necessary to have the code elements memorized and have a very little practice with them. Most people had to practice for at least six weeks to get to fifteen words per minute. As a result of these changes, tens of thousands of new voices appeared on the ham bands this past year.
In order to listen in to most ham radio communications, you need a receiver that is SSB capable. If you see a switch on the front of your radio that says LSB, USB, SSB, Clarifier, or BFO, you've got it made. If not, I can tell you how to use a separate receiver as a BFO, but this is only intended as a temporary or experimental expedient.
In fact, one of the best things about ham radio is that you can use the scientific method to do basic but very practical experiments in physics, such as the above BFO experiment. More and more hams nowadays, instead of learning the theory to pass the written exam, simply memorize the answers (they are referred to derisively as "appliance operators" by some of the more technically inclined hams). That's ok, but they deprive themselves of the ability to experiment and learn. A few of us keep the tradition alive, building or fixing our own equipment, antennas, etc. Occasionally one of us will stumble across a genuine breakthrough, such as the use of shortwaves for long distance (DX) communications, which ham operators first popularized back in the 'twenties. We are, in every sense of the word, amateur scientists. Of course, the "appliance operators" think us all mad. The fools! Mwooo-ha-ha-ha-ha-ha! (For another example of an experiment, and one that worked out well in the real world despite being theoretically invalid, see my note on loop antennas.)
Because many hams are innovators and experimenters, they were some of the first people to experiment with computers and the internet, so there are many hundreds of amateur sites on the Web. I will give a link to only one, the American Radio Relay League, which is the closest thing to an official organization hams have. The others you can find yourself with a good search engine.