Starting off with the spoilerish bit of Sky's ...
I think the bit with Rue is awesome. The similarity of situations of Prim and Rue, that just tugged at Katniss so much. And it allowed some of the walls that Katniss had been constructing around her heart to disintegrate. Rue was someone, I think, who figured that she would just have to outlast everyone, if she was to win. But she helped Katniss locate that nest of Tracker Jackers, which ended up, in an odd way helping to save Kathniss' life. So some bit of walls disintegrated, and then she meets Peeta ... and who knows what might of happened if she'd not met and buddied up with Rue first?
Mostly, to me, this whole section of the book, chapter 13-18, are huge for action and, as Sky says, shows the differences of Katniss' personality, as she interacts with Rue. While I don't think that Katniss would be like Prim, if her father had lived, I don't think she would have become so rigid in her thinking. But then, as she wrote, in talking of her family after her father died ... "all I can see is the woman who sat by, blank and unreachable, while her children turned to skin and bones." That had a huge effect on her emotional health, I think, and maybe in some way, Rue saved Katniss.
*Siggy and Avatar from The Princess Bride*"You have the inborn natural right to remain silent. Don't think about it, don't talk about it, shuush ....STILL."~Xaris