Katniss in the Hunger Games takes the "humble hero" to the next level. Instead of simply downplaying her accomplishments, she sees them as evidence of her character flaws. Deep down, she sees herself as someone interested only in her own (or her family's) survival and therefore incapable (or undeserving) of love. Part of her character growth is learning that she is a person worthy of the love that other give her.
I imagine this kind of character is appealing to children and teens because they, too, are working on some of the same issues. Am I capable? Am I worthy? But, as we know, Harry Potter and the Hunger Games are enjoyed by adults, too. I think the appeal that adults have for these kind of heros is slightly different. We love to see someone who does good because it is the right thing to do--not because they want others to see them doing it. We hope to live up to that ideal ourselves and that others do the same.