Am I the only one who's getting vibes that Katniss is an INTJ?
As for the others:
Peeta: ENFP
Gale: ENTJ
Cinna: INFJ
Rue: INFP
Prim: INFJ (<-- seems like somebody who would have become more J upon growing older)
Haymitch: ENTP/J
Snow - ESTJ
In both Gale's and Haymitch's cases, removing them from the context and into a more normal novel, they certainly come off as ENTP/ENTJ-ish. Haymitch most probably would've been one of those classical 'introverted extrovert' ENTPs.
From the sequels:
Finnick - ENTP (<--- I love him to bits: ENTP relating to ENTP?)
Annie - IxFP
Beetee - INTP
I'm obsessed with typing fictional characters xD Being a writer myself, MBTI has helped a lot in character shaping. I don't agree that book characters seem to have a mixture of personalities, though. From what I've read, most characters seem like they can be attributed to a certain type, but when they start acting like another, that's when the reader starts to feel as if the character is 'unrealistic' or 'acting unlike himself/herself'. A perfect example would be the classical ESTP-bad-boy-suddenly-turned-to-super-compassionate-ENFx-overnight in bad chicklit. Or stoic-tomboy-INTJ-good-girl-suddenly-turned-into-a-giggly-ESFP-ditz. Not to say that everybody who has those personality types has to be like their stereotype, but the sudden change often seems unnatural since they're literally turned into another personality stereotype overnight.