Historically speaking, when a book finds its way on to the big screen there are generally a fair amount of changes. Most of the time its purely done to make the plot move along at a quicker pace so a book can be condensed down into two hours. In my opinion, The Hunger Games franchise did a good job at adapting from book to movie. Suzanne Collins wrote the screen play alongside the director which may have helped in saving the integrity of the book.
The first, and probably most significant, change I noticed was the shifting of the point of view. The book is a first person account of the events encircling the Hunger Games as told by Katniss. The movie depicts the story in a third person point of view. This approach seems to give the story a more dramatic speculation rather than the in-depth analysis and personal account we received in the book. Instead of being able to hear Katniss' every thought, feel her agony, we are given a chance to sit back and witness it. Also, the actual Games are narrated by Caesar. The change of point of view also takes away most insight we received through Katniss. In the movie Katniss and Rue still form their alliance, but we aren't informed that Rue reminds Katniss of Prim, nor how she feels for little Rue because no one volunteered to take her place. The death of Rue, and especially District 11's reaction, is explored in much greater depth. In the book we know only that Katniss receives gifts of appreciation from the district, but in the movie we witness chaos and rebellion. The citizens of District 11 start attacking peacemakers and destroying building starting, and possibly foreshadowing, an uprising against the Capitol. These differences are made possible due to the shifting from first to third person point of view.
Other changes don't necessarily impact the plot the same way. For example, the mutants introduced at the end of the games do not have the eyes of fallen tributes. It isn't detrimental to the plot, but it was an important detail in the book. We see more of Gale in the movie, too.