Non-Profit Local Insurance (a free* idea)
It is quite obvious that a good portion (I'd guess half) of our insurance bills are used to pay for running costs and profits to shareholders. For some insurances there is no reason why a local system could not provide the same function for half the price.
Here's a simple example - bicycles.
An administrator runs the system for free. Every bicycle owner in the town pays $1 a year insurance. Each person who has their bicycle stolen receives $100 to buy a new one.
The above example is extremely simple, and a working system would need to allow for fluctuations (12 bicycles being stolen this year, but only 8 next year), but with some effort a similar system could be used for other items.
It would work best when:
1) Insurance fraud is unlikely
2) Proof is not hard to provide
3) Claims are infrequent
House fires fit the criteria well - they happen rarely, they are easy to prove and it is extremely unusual for people to deliberately torch their own homes.
UPDATE: I've just discovered that our Muslim friends have something similar called Takaful