According to their website, the DNT is Norway's largest outdoor activities organisation. Their work includes maintaining a fantastic network of marked hiking trails and running 144 mountain lodges, linked by these (and other trails).
We have just returned from a week hiking in Jontunheimen and cannot praise the DNT highly enough. I have never seen such an organisation so successful at making the wilderness accessible with minimal disturbance to the natural environment.
The trails are well-marked and maintained and where we used trails not maintained by the DNT, staff were nevertheless able to advise on them. The level of service at the fully staffed lodges we used was extraordinary and not too expensive (by Norwegian standards!). And how good is it to come off a mountain, knowing that a comfortable bed, three course meal, hot showers, and effective drying room are waiting for you? The DNT prides itself in never turning anyone away.
We were walking as a family with two under twelves, so didn't undertake any really major climbs, but the DNT also organises tours of the high peaks etc.
All the activities we undertook, we could have done as non-members, but joining the DNT meant serious discounts on accommodation costs as well as the ability to secure beds when the lodges were nearly full. If you are venturing deeper into the mountains and staying at unstaffed lodges, I think you need to be a member to get a key to the lodges.
I could not agree more with this tip. I followed this tip and have just returned from a DNT trip. Six days walking/cycling through beautiful and unspoilt Norwegian countryside. Yes, Norway is expensive. Yes, the huts you will stay in are expensive (but included in the holiday price). However, when you consider the price of a 5, 6, 7 day walking holiday with these guys they compare very favourably with standard trekking companies. The bonus is the walk leaders are volunteers and dedicated - they really do care. The whole group spoke English (despite non being Brits, a good sign in my view!). The huts were in stunning locations and the meals were on the whole miraculous - homemade bread and jam for breakfast, three-course meals from local ingredients. Guardianista foodies walk, eat and enjoy your hearts out.