In 1998 the Fifty-first World Health Assembly passed the "health-for-all policy for the twenty-first century". During this assembly the Member States of the World Health Organization (WHO) reaffirmed their commitment to the principle that "the enjoyment of the highest attainable standard of health is one of the fundamental rights of every human being". Even if there is now a worldwide consensus that health insurance plans should cover the whole population to attain the highest standard of health, a question still remains unsolved. What kind of health insurance coverage is the most likely to attain this goal efficiently? European countries are frequently cited as exemplary for the high level of health attained by their population, while sometimes very different health insurance models are implemented today in these countries. This paper discusses the advantages and shortfalls of the different options, for health insurance and population coverage that have been chosen in Europe. Four topics are treated successively: the choice between private and public insurance, how to guarantee the balance between revenue and expenditure? What should be the basis for health insurance payment? And finally should health care services be totally free of charge for the patients?