I am not sure that I am exactly like Katniss, but I identify with her because of her sacrifice. She is willing to take her sister's place in the games, and that is something I like to think that I would do in the same situation.
Oooh! Fun! I must admit to seeing myself being a bit like Peeta in terms of the way that he is a good and loving man who stands up for what he believes and also is willing to sacrifice himself for those that he loves. At least, I try to be like Peeta, but as to whether I actually succeed or not, that is another story!
I would have to say Rue. I love nature and find it very comforting. I like her spryness and her simplicity. Other than that, my second would be Katniss. Cliche, I know, but i see a little of her guts in me.