Aside from the insurance coverage, Airbnb appears to reduce risk for involved parties by humanizing the transactions. They encourage getting to know your host, and I'd imagine people are more likely to respect other people's property when they are aware of and can relate to the person behind the space. Even before transactions take place, users are encouraged to have rich profiles and social connections to demonstrate reliability and facilitate trust.

There may be potential for this sort of humanization in other areas where the perceived risk of a transaction currently outweighs the benefit. One way to think about it may be to consider things that you borrow from a friend. Airbnb covers the sleep on a friend's couch/spare bed niche quite well.

Some interesting things I can think of... perhaps using space on a more granular level such as holding a meeting in a conference room or watching a movie on a home theater system. Things like renting parking spaces might be interesting as well in some areas where parking is very limited.