Car insurance doesn't protect you, it protects the other drivers on the road. You can decide to risk it, and if your brand new car is totaled, its on you [assuming you paid cash, if you finance it any lender will also make you get collision and comprehensive]. What you can't decide to do is forgo liability insurance so that if you hit someone else's car they have to extract the payment from you rather than from a well-capitalized insurance company.

Of course this is all state regulated (and this is US-centric, but so is Obamacare), so it can work differently in different places.

Health insurance nominally protects you, though some make the argument that it protects society as a whole from any individual burdening the system.