Jane Galt, a writer at The Economist, has a theory why the market for health insurance does not work that well in the United States.
My suspicion is that the employer health insurance system has prevented the emergence of reliable brands. Almost no one has any control over their health insurance, so there is no incentive for companies to develop a reputation for speedy resolution of problems. You can't ask your friends about their insurance. There's not even good reason for companies to give you good service as a private consumer, since you will leave them as soon as you get a job with benefits, regardless of how well they perform. And if you move across state borders, you'll hit a new regulatory regime, which means you'll be buying an entirely different produce anyway...
So I'm not sure how big a problem adverse selection would be in a normal health insurance market. The problem is, we don't have one; we have a system where a few desperate and unreliable consumers are trying to buy insurance from a few desperate and unreliable companies.
The big question that is currently unresolved is whether a market can be established that would allow consumers and producers to replicate an optimal market outcome for health insurance. The current problem with the US is that health insurance is tied to your employer. Most people under the medicare age limit are insured via their employer (as are there kids). If you do not participate in the employer based health care system, you are at a loss because there is no pooling mechanism to lower the cost of insurance. Add in state and federal regulation and, depending on the state, individual premiums can be very costly (although on average this may not be the case).
So, we either dismantle the entire system and put a government run system in its place (an idea that the original article I posted below dismantles, I believe) or we come up with another way of pooling consumers so that we can have an individual market. I have heard of at least two ways to do this.
a) Have the government provide a health adjusted voucher to consumers to purchase insurance (that is, if you have cancer you get a large voucher. If you are healthy you get either a small or no voucher). Then let the market work its magic
b) Set up a pooling mechanism where customers can purchase insurance. Customers would not purchase insurance directly from the insurance company. Instead, they would purchase the plan via the pool and then the pool would aggregate the customers and negotiate terms with the insurance company.
Of course, the Ideal libertarian/free market solution would be to remove any and all incentives for health insurance and use tax free health savings accounts (perhaps with government matching/funding for the poor) and then let consumers buy their health care directly. However, while interesting I believe that this solution is not politically realistic.