It varies a lot by country. In Denmark, all hospital visits are free to anyone, whether a resident or visitor. In other countries, non-EU visitors to an ER might pay substantial amounts, though usually still quite a bit less than in the US. Also, some EU countries tie insurance to payroll-tax contributions, so the unemployed may not be covered.
Well, been living in 4 European countries and never paid anything but in mine (Italy). I am also pretty sure unemployed are covered too. Don't know in Germany, where I still can't get how insurance works, but I would guess there is a way to get cover there too.
