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In Norway you are free to hike and camp everywhere, even on private ground. You can't pitch a tent closer than 100-200 meters to a building, and you can't stay at the same spot for more than two days.
There are also hundreds of cabins spread around the country owned by the tourist board. Some big ones with room/bed rentals and food serving but most are smaller and unmanned. Some of the unmanned cabins will even have a food storage you can take whatever you need, write it down and they'll send you a bill later. Membership is super cheap, and for an extra $20/year you get your own key that will open all the hundreds of cabins.