Wow, there are two cables running from northern Norway to Longyearbyen, on the island of Svalbard! According to Wikipedia, "Longyearbyen has approximately 2,060 inhabitants (at the end of 2007..." The total population of Svalbard is not much more.
The reason for that is there's a an important satellite ground station on Svalbard - it's in an ideal place to communicate with polar-orbiting satellites:
Photographer Christian Hougue produced a really beautiful series on this ground stations called Arctic Technology. He mentioned that the air is some of cleanest in the world, which is a real boon to the equipment they're running.
Edit/Add: The cable length is 2,714 km.