In Norway and Sweden you are allowed to move around and to stay on uncultivated land - i.e. woods, moors and mountains - all year, and even on cultivated land during winter. You also have free access to all beaches, except where the beach is a part of a built up lot. You should not go within 150 metres of any building.
Apart from these restrictions, you are allowed to go anywhere on foot, bicycle, horseback or skis. Motorised travel is only allowed on roads, and private owners may close their roads to traffic or charge a fee. You are allowed to take your boat along the coast, on lakes and on watercourses. You can moor anywhere, except at private lots or boat landings. Motorised boats are forbidden on the smaller lakes. You are allowed to swim wherever you like. You are allowed to stay overnight - i.e. put up your tent on uncultivated land or park your campervan along the roadside - wherever you like, as long as you do not damage anything or hamper professional activities. However, without permission from the land owner, you are only allowed to stay for two nights.
You can freely take water from the springs and lakes. Most of the water in the smaller lakes and creeks is drinkable. You are allowed to pick flowers, mushrooms and wild berries - except for cloudberries in northern Norway. Game fishing in the sea, lakes and rivers is generally permitted, but freshwater fishing requires a payment to the government and/or to the land owner or his representatives.
However, the public right of access to the countryside gives you freedom with responsibility. You should not in any way damage the natural environment, you should show consideration for professional interests, and for other countrygoers. You should not trample fields and meadows, damage fences, break off, cut or in other ways damage trees and other plants, or disturb animals. Water supplies should not be polluted. It is forbidden to use open flame or light a fire from 15 May to 15 September except in specially designated places and on bare mountainsides. Dogs should be leashed and kept under control. However, dogs may go unleashed during the winter season. Observe the strong regulations for bringing animals into Scandinavia - they are there in order to keep Norway and Sweden free of rabies.
Read more about the Right to roam published by the Norwegian Environment Agency.