The News and Observer has an article promoting Singapore as a reform model for the U.S., and the article laments that Canada and Europe seem to be the only places people look if they want to look at other systems. There are at least 3 Asian systems of note:
(1) Singapore has a gov't catastrophic plan, give gov't support to low income folks to purchase private health insurance, and is well known for use of health savings accounts. There article in the N and O is here http://www.newsobserver.com/opinion/columns/story/1629555.html. Singapore is quite an idiosyncratic place, and while individuals being involved in their own care is a libertarian goal, Singapore is one of the least libertarian places on the planet. Or maybe they make you be libertarian? In all seriousness, it is an example of incentivizing people to think about their health care expenditures...and is the anti-thesis of the U.S. upside down subsidy of private health insurance via the employer paid tax exclusion.
(2) Japan has a social insurance model with an insurer of last resort linked to geography, sort of like if county's insured all persons not otherwise covered. If Singapore is an attempt to de-link insurance from employment, Japan is heavily linked to employment (though you remain covered if you lose your job). Individuals are covered via payroll tax financed sickness funds that are insurance pools (Germany is based on this notion as well). Large employers self insure and run their own fund. Employees of smaller employers are placed in different funds, and there is a specific fund for civil servants. Co-pays are fairly high until one reaches age 70 and then are quite low. Private insurance is not a part of the mix.
Japan (along with Germany) has made the biggest changes in financing long term care over the last decade, with Japan creating a system that was designed to replace informally provided (family) care with care purchased via a gov't program. Essentially the goal of the reform was to address gender inequities and 'crowd out private care' with public money. The bill that created the reform was called the 'daughter in law bill.'
(3) Taiwan has a tax financed single payer approach, essentially US Medicare for everyone. One interesting aspect of Taiwan's system is that it covers western medicine along side of traditional chinese medicine. There is priviate coverage for gaps in coverage similar to medigap in USA.
There are some huge demographic differences in these nations... Singapore has 8.5-9% of the population 65+, USA has about 13% and Japan has about 21%. Also, Singapore is filled with guest workers who get deported if they get sick. But, still an interesting model.
So, there are models of note in Asia. Quickly you find an example of lots of private individual involvement (Singapore), a social insurance model (Japan), and a single payer (approach). Sorta like if you look at Europe and Canada.
All intersting models, but there is no magic bullet.