New Zealand has a comprehensive no-fault insurance scheme administered by the Accident Compensation Commission (ACC). The scheme applies to all injuries incurred in New Zealand regardless of the injured person’s country of residence. Under the ACC scheme it is generally not possible to sue for damages due to an accident. To pay for the ACC scheme, levies are payable by all New Zealand resident employers, employees and self-employed contractors.
In other words, instead of being able to sue another party, you get a piddly payment from the government. Here is material on the history of ACC. Here are more details, along with accident statistics. You can buy a law review issue on ACC. Here is one criticism of ACC, from a market-oriented point of view. It is, after all, government monopolization of the accident insurance market. On the other hand, it keeps down lawyers’ salaries.
Here is further information on the safety of bungee jumping.
Addendum: Libertarians who hold great faith in market mechanisms of reputation might favor this system over strict liability. Consumers could still patronize a high-reputation, high safety bungee-jumping firm, if they wished to, thereby replicating strict liability outcomes. But other consumers could opt for the "I don’t mind not being able to sue you, anyway I know you otherwise wouldn’t exist and I love risk" kind of ride. Of course this split will work better for contractual relations than for road accidents.