In Germany everybody who is employed in way that pays social insurance is also health insured, you cannot opt out of it. In that system, in addition to taxes, social security and unemployment insurance, you pay a certain percentage of your gross salary to get health insurance. This percentage varies by your choosen provider. Your employer is paying the same amount (more or less, not sure if the employer amount is fixed). You can opt out of the public system above a certain salary and pick private insurance, prices vary greatly.

Unemployed people are insured by the state, I guess using taxes or social security or unemployement budgets, I have no idea. You have to be registered as unemployed to be covered. If you do not register you have the choice of being insured with a family member (public health care) or voluntarily (private or via the public system). You are obliged to be insured oine way or the other.

Exceptions are soldiers (some kind of in-service system with cost reimbursement, don't ask for the details), public servants (something similar in a lot of cases, again, please don't insist on details), certain professions (doctors, pharmacists, artists,lawyers) with their own insurance solutions. You are screwed as a afreelancer, your only solution is a private insurance that can get quite expensiver.

TL/Dr: You are always insured one way or the other. It is not paid for by taxes.