You don't have to have health insurance. You have to pay a fine for not having health insurance. Many people decide that the fine is the cheaper option, so health insurance companies at least have to compete with that.
You don't "have to" do anything under the law. Nobody comes and holds you by the wrist and makes you do it. You just have to pay fines, or go to jail for not doing it.
To drive on the public roads you have to prove "Financial Responsibility" for most people the cheapest and most effective way to do that is Auto Insurance, however every state i am aware of has alternatives, aka "Self Insure" that can be a Bond, or some other guarantee that you are able to cover the minimum liability of state