James Newton Howard
You've probably seen the name James Newton Howard on a number of movie credits before. He's one of those post-John Williams guys who's scored everything from M. Night Shyamalan films to the Julia Roberts vehicle Pretty Woman, that Peter Jackson King Kong remake, and the Christopher Nolan Batman films (which he tag-teamed with Hans Zimmer).
Howard grew up in Los Angeles and showed a knack for music at an early age. That wasn't surprising, since his family consisted almost entirely of musicians. Probably USC's most successful music school dropout, he started his career in rock and roll, and actually played keyboard back-up for Elton John for a time. (This is in keeping with other film composers of his age, such as Zimmer and Danny Elfman, who also come from rock-and-roll backgrounds).
Howard's composing career started out in the 1980s, with immortal films like 8 Million Ways to Die and Russkies. He soon earned a reputation for cranking out scores very quickly, which led to a steady career of two or three movies a year, every year, for a quarter of a century. Along the way, he picked up an impressive 8 Oscar nominations, though he remains a bridesmaid on that front with zero wins so far. But he keeps on trucking, with more scores listed on his resume as of this writing.
With The Hunger Games, he created two distinctive musical motifs. For Katniss and District 12, he goes with strings, giving an Appalachian flavor to the themes and an infusion of folk music into the vibe. That makes a lot of sense, since the District 12 folks don't have a lot of entertainment, and (as later books and movies in the saga make clear) folk songs are about all the culture they have. There's a lot of fiddle and banjo mixed in to it. Take a listen here.
With the Capitol, it's all pompous brass noises: propagandistic tunes intended to imply strength and a unified will. It's supposed to be inspiring but there's an air of menace to it too. Take a listen to the Capitol's anthem. You hear it a LOT when they bust out with the parades and the marches. (The Canadian indie band Arcade Fire actually composed the Panem anthem.)
With those two themes as the base, Howard goes on to infuse some serious scary into the mix. This isn't exactly a pleasure cruise for Katniss, after all, and Howard wants us to know how dangerous it all is without losing the thread of his main themes. So you can pick up a lot of low, ominous tones laid beneath the the brass and the drums of the Capitol. He'll occasionally ramp that up to keep our pulses pounding when terrifying stuff happens: mutant dogs, Careers with knives, cocktail parties, etc.
If you listen closely to the score, you'll see that it doesn't overwhelm the story, just gives it a little boost. For a movie about children hacking each other to death or being torn apart by mutant dogs or bugs, Howard shows a lot of restraint (source).