This cult site puts budget travellers in touch with people who are willing to let someone stay on their sofa or in a spare room, or otherwise offer a friendly face in an unknown destination. Free to join, it has a useful members' reviews facility and operates a circle of trust - users are vouched for by existing members - and, on the host's part, there's no obligation to let someone stay if you don't like the sound of them. Other security measures include a name and address verification scheme.
Like that? Try www.warmshowers.org; www.hospitalityclub.org; www.bewelcome.org