Nearly every book has a protagonist, but they don't all have heroes - not real heroes. There are two definitions of the word:
hero - hɪəroʊ –noun, plural -roes; also -ros.
1. a man of distinguished courage or ability, admired for his brave deeds and noble qualities.
2. the principal male character in a story, play, film, etc.
But being the second doesn't make a character the first. In ancient literature the leading player was almost always a hero - a great and courageous fighter, like Achilles for the Greeks or Cu Chulainn for the Irish. "Noble qualities" did not necessarily entail high morals; rather they were those virtues that were considered manly, like cunning and daring. If a man made a name for himself through his warring exploits, through the taking of more booty and spilling of more blood than his companions, he was a hero.
The influence of Christianity has changed the concept of "hero" in real life and literature. Take superheroes, for instance. Sure, they have great powers and strength, but they are not given the title "hero" unless they use those powers for "the greater good." Those who use their powers for their own ends are villains, whereas in the ancient epics, most of those men who were called heroes were focused wholly on self-aggrandizement. I'm currently reading The Odyssey, and Odysseus is a prime example of this. I had always thought that the story was about him facing the odds and enduring hardship to return home to his wife and son. Not the case. He kind of dawdles around the Mediterranean, collecting loot; spending a year with Calypso, then a few weeks with Circe; collecting more loot; and then finally deciding that he might as well head home to his own land now. But his wiliness and courage make him a hero by the Greek definition.
The difference between how we view a hero now and how he was viewed then can actually be seen in Disney's "Hercules," where Hercules progresses from "zero to hero" by the popular definition, but never becomes a true hero until he sacrifices his life for Meg. Being a hero means more than defeating your enemies; to be a hero is harder than that. It is easy to kill, but harder to show mercy. It is a simple thing to destroy, but a harder thing to exercise justice. Even gaining riches is easy compared with the hardship of giving up everything for another.
Some of the best tales are ones that combine these two elements of a hero. Adding the thrill of a victorious warrior to the depth of a godly man makes a truly great character, like David. Not every protagonist will be a fighter, but every hero ought to that inward strength that sets him apart as a great man, a man who reflects Christ. For who so completely embodies the heart of a hero as our Lord?