The turf roof, or 'torvtak', used to cover houses in Norway since at least 500BC, used birch bark shingles covered in peat or turf sods, over which grass, flowers and other stuff grew. An illustration of Bergen in c1580 showed sheep grazing on the city's turf roofs.
 
Green roofs gradually fell out of favour as public buildings and wealthy families started to use tile and slate. In 1624 they were eventually banned by King Christian IV in Christiana, although more rural northern towns such as Trondheim many houses still have turf roofs in the 18th century. By the 20th century green roofs were on the wane, although in Hornindal three-quarters of all houses still had turf roofs in 1933. Continuity of the tradition continued in open air museums of building, and in the past few decades green roofs have seen a big revival not only in rural and traditional housing but on modern city buildings too.
 
See torvtak in Wikipedia for more technical info on traditional Norwegian turf roofs.