Don't most of those "free" public health care systems only apply to citizens? I recall a story about a foreigner in Germany having to pay for their care, even if the price was reduced. Non-emergency care in the UK, for example, requires legal residency, which may be hard to come by for someone too poor to afford health care in the US. France requires non-EU citizens to have insurance for care in France to get a visa, as I understand it.

So, it's not just as easy as "let's pack up and move to the EU so we can get free healthcare tomorrow." Otherwise, you can imagine that every time a non-insured American got sick, they could compare the cost of getting new insurance to the cost of a plane ticket, and the plane ticket would win, I'm sure. =)