If you want to filter your/your child's movie viewing through some fairly granular rules about sex, nudity and profanity, the Motion Picture Assocation of America's rating system is your friend. If, like me, you have a weak stomach for depictions of violence--glorified or not, realistic or not--you kind of have to do your own research. Over the years, the MPAA has made pretty clear its position that bare skin and naughty words are bad for the kids, but people getting disemboweled or blown up? Meh. (This is all well documented, most notably by the film This Film Is Not Yet Rated.)
The Hunger Games is rated PG-13. Bully, a documentary about bullying in schools, was going to be rated R (for language) until the studio decided to release it unrated intead. That's right: according to the MPAA, a fantasy about kids murderously hunting each other down is more appropriate for kids than a doc aimed at drawing attention to the destructive power of cruel words, one of which happens to be the word "fuck."
Richard Corliss provides some background and context on this troubling juxtaposition, along with reviewing the two films (subscription required). See also Andrew O'Hehir's piece on Bully and the MPAA, and my colleague Janet Potter's on how The Hunger Games tries to have the violence thing both ways.