I am not sure about the USA but in several European countries squatters right exist but are limited.
You can move in a house that hasn't been lived in for a long while, has no furniture etc. and you can stay (you can ask for water and hydro to be reconnected and you will pay the bills).
However if there is an owner--or heirs--still living somewhere in the world he/ they have the right to kick you out, but not that easily.
You can't be kicked out in winter (I am still talking about Europe), the owner must find you a place to live that you can afford etc.
There has been cases when someone had lived on a piece of land for over 30 years in a small shack they built. There were no owners alive, and when a company wanted to expel the guy and buy the land they lost. He became the legal owner.
In Paris some companies that owned a building find it cheaper to let squatters stay there officially rent free as long as they take care the place as if they owned it. However they will eventually have to live. Also I am pretty sure that it applies to citizens of a country only.
If you were a foreign tourist and decided to stay forever you would become an illegal alien. You might be able to stay if you hide deep in the forest but, surely, as soon as you start going down to a town to get stuff, people would be suspicious..The smaller the town the faster the likehood of an illegal stranger to be discovered.
it is possible in Europe--and that is better than squatting--to buy a place in the boonies or sometimes in a town, that is just 4 walls and a roof, has no electricity, plumbing etc. and cost may be $ 10 000. It is up to you to do all the work to make it fit to live in, and this doesn't have to be overly expensive. But, again, you must be legally allowed to live in the country.
This is what you get for Euros 27 500 in a small town http://en.century21.fr/trouver_logement/detail/378925844/