Loyalty is an important theme in the novel The Hunger Games written by Suzanne Collins. The theme is present in the entire series as well.

Throughout the series, Katniss Everdeen exudes loyalty. She is loyal first and foremost to her family. Katniss takes care of her mother and sister by acting as a parent-figure. She cleans the house, hunts for food, and trades for goods. A major point in the story where loyalty is shown is when Katniss wishes to protect her sister, Prim, and therefore volunteers herself as tribute to participate in the games.

Once Katniss arrives at the games, she must remain loyal in her alliances with other competitors in the games in order to survive. Katniss is especially loyal to Rue, a young tribute, and to Peeta, the male tribute from her district. Katniss shows compassion for Rue after Rue's death by singing to her and covering her with flowers. Katniss proves her loyalty to Peeta when they are the last two remaining tributes and must decide who will live and win the games and who will die. Katniss creates a plan where both her and Peeta can survive or they can both die and ruin the games entirely. This moment is a pivotal point in the series because it sparks the rebellion against the Capitol that is led by Katniss.

Katniss is loyal enough that she is willing to sacrifice herself for those in her life who are important to her.

How is loyalty shown and important in The Hunger Games?

The theme of loyalty is shown throughout The Hunger Games. First of all, when Katniss Everdeen, the protagonist of the story, hears her twelve year old sister Prim's name called for the lottery, she chooses to replace her in the Hunger Games.  This is clearly an act of loyalty.  Katniss knows that her sister's gentle nature would be her demise in the games and chooses to sacrifice herself to protect her. 

Peeta shows loyalty throughout the book to Katniss.  First, in chapter two, Peeta literally saves Katniss's life several times in the novel. First, he saves her life when he intentionally burns bread in the family bakery and risks his mother's wrath.  This is done so that he can throw it to her, and it literally saves her life.  Peeta's elaborate plans to protect Katniss in the arena clearly demonstrate his loyalty to her, although she doesn't always realize.  By teaming up with the Careers, Peeta actually saves her life in chapter 14.  Later, Katniss repays him by nursing him back to health.

Katniss also shows loyalty to Rue, the girl in the games who reminds her of Prim, her sister.  Rue watches over Katniss after she has been attacked by tracker jackers and is hallucinating.  After, Katniss shares her body heat to keep Rue warm after.  Later, when Rue is captured in a net and speared by a Career, she risks her own death by singing to Rue until she dies.  Rue's favorite thing in the world is music, so this eases her passing.