The Hunger Games has been likened to the 1987 movie, The Running Man, starring a few US Governors. Stephen King ghost-wrote the book that The Running Man was based on. King is a big fan of Suzanne Collins' work, so I take that to mean he doesn't take much offense at any similarities.
There are a few key differences between the two stories though. The Hunger Games rely on teenage "tributes" chosen by lottery, innocent of crimes and it is used as a means of control and reminder of the power of the Capitol. The Running Man game is played by convicts (mostly adult men) and is used as purely a form of entertainment for the masses; they chose strong men who would last longest and get the best ratings.
The Running Man is an instantaneous survival game broken into segments where famous and elaborate executioners hunt down the running man/men. It's usually completed within a day. The Hunger Games has an immediate death toll, as the tributes try to grab supplies and run to safety, but most of the game involves days and weeks. Time becomes an enemy as food, water, and basic survival in the elements can become the real killer of the tributes.
For both stories, if the tributes/victims aren't dying fast enough, the Gamemakers will manipulate the game to increase the drama (ratings). In the Running Man, it is the executioners in elaborate scenarios (like an ice rink). In the Hunger Games, it is the use of weather (rain), fire, or "mutts" (genetically manipulated creatures intent on specific tortures). The movie Running Man is more campy than the Hunger Games, with Arnold giving cheesy one-liner jokes after every kill.