Another thing Iceland is known for is its unique telephone directories...
Nearly all Icelandic surnames end in either "son" or "dottir". This is because in Iceland, a person's surname is generally derived from their father's name and their gender. So if someone named Karl Magnusson were to have a son, his son's surname would actually be Karlsson. If Karl Magnusson had a daughter, her surname would be Karlsdottir.
While family names are inherited in most countries, the way to keep a name in your family in Iceland is to pass on your first name. In order to keep a name, Magnusson, for example, in the family, fathers throughout the country must keep naming their sons Magnus. It is for this reason that the Reykjavik telephone directory literally has pages of listings for Magnus Magnussons.
While one would figure this would probably result in massive confusion whenever an Icelander tried to do something as simple as place a telephone call, since Iceland has such a small population, they've found a way to get around that. If you look at an Icelandic telephone directory, it will not only state the person's name and address but will also state a few facts about the person, such as "about 5'4" tall, works at the bookstore", etc.
thanks to paladeen for clearing up a few points. if you're interested, see Icelandic Naming System for more information.