Servas
This word, servas, means service in Esperanto. This organization walks a thin line. It is dwindling in size, but hesitant to advertise lest it attract the wrong people. So this information has the same slant. If you travel anywhere, you should know about Servas, but you should not be the type to abuse it.
Servas consists of a worldwide body of travelers and hosts. Not all hosts are travelers and vice versa. You get the idea. So you join Servas with the hope of meeting people from around the world, either by being a host or traveller. To join, you need to be interviewed by a local member who has agreed to give interviews. You can get a list of these people from the website. Basically, they want to make sure that you really are curious, kind, and full of empathy for other cultures. Assuming you are, you'll pay a small fee that covers administrative costs and they'll mail you a book for your country, if you're a host, or the host lists for the countries you intend to visit if you're a traveller.
Servas hosts are mainly found in Europe, North America, and Australia/New Zealand. There are also hosts in Asia, but these require a lot of advanced notice and are subject to change. Frequent change. In China, current law forbids foreigners staying with citizens, so all hosts are Day Hosts, which is something you'll find throughout the system and basically means the person is willing to show you around town if during the weekend and perhaps have you over for dinner. Not a bad thing.
As for making the visit worthwhile, try not to be overly apologetic or gracious about anything. This is an exchange, and try to make it that without just being a gushy guest or host. Life experience is being exchanged. People join Servas precisely because they want to exchange this. You can find their international website at www.servas.org.