The Hansen family was the family of Annika Hansen, later known after her assimilation by the Borg as "Seven of Nine".
In the 22nd century, one of the Hansens' ancestors was Sven "Buttercup" Hansen, a boxer. (VOY: "11:59")
Annika was the only child of her parents, named Magnus and Erin. Her father had at least one sister, Irene, who lived on Earth. (VOY: "The Raven", "Dark Frontier", "Author, Author")
Another supposed aunt of Annika, named Claudia, apparently wrote a letter expressing her eagerness to meet Annika, but she turned out to be a fictional creation of a bio-plasmic organism encountered by USS Voyager in 2375. (VOY: "Bliss")