The Hunger Games series is most obviously related to any number of dystopian novels. It could be taught in conjunction with the graphic novel V for Vendetta, or with dystopian classics 1984, Fahrenheit 451 and Brave New World. It would also likely be beneficial to look into YA adventure stories about guerrilla warfare, such as the Australian series Tomorrow When the War Began. One could also teach it alongside novels like Station Eleven, which depicts the search for meaning in a post-technology world.
Catching Fire also deals with crushing poverty and inequality, something that could be taught in parallel to Steinbeck's The Grapes of Wrath or to nonfiction works like The Glass Castle or...