I have been a shortwave listener for many years (as well as an amateur radio operator). In fact, when I was in Junior High, I rebuilt an old radio using the "new" (in the 1950s) miniature tubes, and it worked better as a shortwave receiver than as a regular radio! I learned to solder, read schematic diagrams, find parts wherever possible, and troubleshoot!
I had great fun with all that, and was excited to get a used S-38 (the original) which I used in my first ham radio station. I kept a log for several months before I got turned on to ham radio. In the last several years, I was given a Drake SPR-4 Communications Receiver (a radio I had drooled over in the 70s), complete with the previous owner's shortwave listener log! Good radio--first transistorized one Drake offered--read about it on the link above.
I was a regular listener to the BBC, now on public radio stations in Colorado. I was disappointed to hear that they discontinued their shortwave service to North America, but the signal is of course pristine on local FM! Occasionally I've listened to Radio Netherlands (now discontinued, too), CRI, China Radio International, and Radio Australia. I have also heard Radio Sweden in a short broadcast to North America. When the Sun is quiet, the 49 meter band (5950-6200 kHz) has usually been best.
You can visit PrimeTime Shortwave's web site for tons of good links. One of the links, Radio Reference, even has live audio feeds!
Voice Nation has lots of good links for exploring the world of Ham Radio. The largest organization of, by, and for hams, the American Radio Relay League, is a great site for everything related to radio communications. Here are the frequency allocations for ham operation.