Children of Men is an excellent dystopian cinema piece concerning the idea of human extinction through infertility. While this may seem interesting, I'm sure the reader is thinking "What does this have to do with the Hunger Games?" Well, it turns out, quite a lot! The militarized government of Great Britain is not unlike the heavily regulated districts of Panem, where the government attempts to keep the lesser people down through intimidation and violence. This results in an uprising that claims many lives as the people try to reclaim their freedom from oppression.
Also, both works focus on hope and the effect it can have on people. The idea that there could be a cure to infertility is the central mechanism of hope in the movie, while Katniss herself and her defiance are the personification of hope in the Hunger Games. While some look to exploit the hope for themselves, others simply take it and use it for what it is: a symbol that things can get better.
Similarly, both protagonists are everymen, although I suppose Katniss is an everwoman. Neither wanted to be a hero, but they found themselves thrust into the center of a conflict and asked to accomplish amazing things. Both characters had suffered traumatic deaths of people they cared about and both had to defend somebody from outside forces that looked to harm them, with Kee and Peeta playing these roles. Ultimately, both characters accomplish their goals of bringing hope to the masses and keeping the idea alive, whether it be a newly born child, or Katniss herself as the Mockingjay.