Singapore - arguably the most efficient healthcare system in the world. Tim Harford talks about it in his excellent book "The Undercover Economist" (worth commenting that he's not rampantly free market - he spends time putting the boot into the US system too as well as praising the UK's NHS).

Basically everyone has to maintain a fund (the government pay into it for the poorest) for healthcare. This is what they spend when they have healthcare needs.

Because the people are making the purchasing decisions themselves (as opposed to the insurance company doing it) they have a far stronger incentive to demand value and to be informed, and you get genuine competition between providers (as if you don't like them this time you'll go elsewhere next time with no insurance company mandating who you can see).

The government then picks up the few areas that aren't well catered for by this system.

I think it costs about 40% of what the US system costs (possibly even less) and Singapore has a typical life expectancy of 80.