In Season 3 Episode 6 Sansa is dragged all across the story, for who she's supposed to marry. I don't quite understand why she's so important. Because there is her brother Rob, who is the King of the North and Lord of Winterfell. And if he fell wouldn't all of that go to Bran (although he may or may not be alive according to their knowledge)?
Bran is believed to be dead. When Robb marches to war, Theon Greyjoy betrays the Starks and takes Winterfell. Bran and Rickon escape. Theon eventually has two boys slain at a farm and says that they were Bran and Rickon. As far as the greater world knows, all the Stark men are dead, which leaves Sansa (the oldest girl) as the heir to Winterfell. Whoever marries her will become Lord of that region.