Dragonlich

In the Netherlands we have (near-)universal healthcare, with compulsory insurance. The government sets the minimum coverage, the market decides the fee. The current monthly fee is around 90 Euros a month for the basic package. People can get additional coverage (non-essentials such as dental care, glasses, physical therapy, etc), for an extra X euros a month.

This system has led to a mild increase in competition between the insurance companies. The basic price is pretty similar for all companies, so it's not perfect. But that was to be expected, given the basic package. There's more competition with the extra coverage plans, and additional service.

Because of my work in various hospitals, I know that there are some problems with illegal immigrants. They must get treatment, but can't get insurance. Some hospitals introduced a cash payment system for these people (apart from the ER, of course).

FYI, people generally aren't too happy with the new system. Before it was introduced two years ago, "poor" people would pay much less, while "rich" people would pay more. OTOH, these days, the poor get compensation, while the rich don't.
For me, the price has gone up quite a bit (40 to 100 euros). I don't get compensation, because I make quite a lot more money than I did two years ago. I can't complain.

Oh, and ASU2003: no, the fee doesn't cover medical insurance. Doctors and hospitals make more than enough money to pay for that. Also, we don't have too many malpractice lawsuits and payments. IMO, that's mainly an American problem.