Norway was a country on the Scandinavian peninsula of Earth's Eurasian continent.
According to Jonathan Archer, it harbored no tropical diseases, which made it a good vacation spot for people who wanted to avoid such medical issues. He suggested that Hoshi Sato take some R&R there after the Xindi crisis had been averted. (ENT: "Zero Hour")
In 2327, the Human William Samuels, who would later become a member of the Maquis, was born in Bergen, a city in Norway. (DS9: "The Maquis, Part I")