A hospitality network is an organization designed to allow cheap and culturally rich travel. The central idea is that of connecting people who are traveling to some place with locals who want to help them. Most of these networks are centered around hosting, that is, giving someone a place to crash. They are meant to be a more interesting alternative to hostels and hotels. Some also focus on culture exchange and have features similar to online social networks. Use these when traveling to meet local people and get shown around and also to reduce accomodation costs. Most have some sort of reputation system to establish trust in people.

The ones I am aware of are:

• HospitalityClub - the biggest one, with 300k members or so, but very limited in features and on slow servers. This one is most likely to have members in obscure places, such as Antarctica. Also big in Europe.
• CouchSurfing - more social-networish than HC, with somewhat fewer members but still rather big. This one is popular in Spain and North America, and some parts of Eastern Europe
• BeWelcome - a new group, focusing more on cultural exchange and web2.0-ness, very small at the moment but growing fast
• Amigost - a more formalized network, with a currency model for reputation. Also very new, and currently small.