This is an interesting question. Since you're from Norway please keep in mind that my post is written in reference to current insurance policy in the US. I can't speak for other countries, but I assume you don't need health insurance in Norway because its provided for within the tax base.
Personally, I do have health insurance which my workplace offers for free, as well as auto insurance as its required by law for vehicle owners.
But, if I had to pay for health insurance I'm pretty sure I wouldn't. Here's why. Its not because I feel like I don't need it, though there is a bit of that, mainly its because I find the modern insurance industry to be a very poorly ran system and I don't wish to support it fiscally.
I used to work at a large (Fortune 100) insurance company as part of their executive IT helpdesk. My job was to fix computers for executives who had the title of "director" or higher, so I spoke to many of the executives there, about 20-30 a day. Two things really stood out to me. First, it amazed me how wasteful the company was. Any simple project, something like adding three lines of javascript to an intranet page, had to be approved and written up by multiple levels of management. Meetings, presentations, and proposals were rampant, and very little actually ever got done.
At any normal company that kind of inefficient management would result in an almost immediate drop in revenue but insurance companies are different. They have guaranteed income from mandatory auto and mortgage insurance premiums. Then if a real disaster strikes (Katrina) they can lobby the government to step in and bail them out with tax dollars. What a racket.
Second, it was notable how unhappy the long term employees seemed to be. Even though they were working at this huge, well-respected company, one of the best paying jobs in Ohio, none of the senior staff seemed happy to be there at all. In fact, almost all of them seemed downright depressed. It seemed like there was a direct correlation between tenure and wellness; the longer people had worked there it seemed the more unhealthy they looked and the less personality they had.
I consider the insurance industry to be something like the modern equivalent of the mafia. You have to "pay for protection" or else you might lose your license, your home, your health care, etc. Thanks but no thanks. I don't need to purchase "protection" offered to me with a gun and a promise that, "this is what's best."