'Allemansrätten' is the Swedish word for all men's right, or better said, the Right of Public Access.
The traditional Swedish thoughts about freedom have led to the fact that everyone has unlimited access to nature. This old law called allemansrätten is even part of modern Swedish law and order. It gives everyone the right to roam freely in nature without having to ask permission of the land owner. Camping is allowed anywhere but in gardens, newly planted tree areas or cultivated farmland. Allemansrätten does have some restrictions towards camping though. You cannot put your tent up next to a house (privacy is important in Sweden as well) or anywhere where you would damage fauna or flora. To really stay somewhere for more than one night you do have to get permission of the land owner. Another restriction is that everyone must close any gate that is opened, clearly to keep animals in the right place.
Allemansrätten allows one another to swim everywhere. You can also tie up your boat at any place, except for private gardens and houses. Free fishing though is prohibited, as most of the times you'll need a license. Hunting is prohibited, period. As far as these plants are not protected, one can pick berries, mushrooms and flowers freely.
Free public access does not mean you can drive your car through natural beauty. The law is meant for people (on foot), so it forbids car and motorcycle drivers to leave the road. Because of the many, many woods, Swedes are not so fond of people setting fires on every occasion. It is forbidden to light a fire on any spot with the even the slightest of hazard in this respect. In case you light a fire, allemansrätten expects you to smother it perfectly afterwards. As speaks for itself (but not to some people) leaving litter is not allowed.
The Swedish Environmental Protection Agency watches the obedience of allemansrätten closely. You can find them online at http://www.internat.naturvardsverket.se/.
TeknoHog says: I think the right applies in all nordic countries, at least it does in Finland where it's called 'jokamiehenoikeus'. Furthermore, multiple people added that the allemansrätten is one of the coolest things about Sweden.