Being brave in the Naruto franchise, or at the very least exhibiting a level of fearlessness in combat, is almost a necessity. All of the main characters are trained fighters who find themselves embroiled in the middle of a war. They wouldn't be able to survive the events of the series - and indeed, some of them don't - without bravery and skill.
Some fans might mistake recklessness or self-assurance for bravery. For example, Konohamaru is quick to rush into fights as a child that he isn't prepared for. He isn't brave, just overestimating his own skills. Likewise, Orochimaru is one of the most accomplished shinobi in the series, but he isn't brave either as all of his work is built on his fear of death. These shinobi, however, demonstrate what it means to truly be brave in the world of Naruto.
Shikamaru
Shikamaru spends a good chunk of his childhood avoiding conflict, not because he can't handle it, but because he is, by his own admission, lazy. His skills and his ability to strategize on the fly, however, make him a brilliant fighter and team leader as he grows. If he wanted the position, Shikamaru would make a great Hokage as an adult, but he'd never throw his hat into the ring for it.
Shikamaru demonstrates his bravery in the field over and over again in the series. After the first mission he leads ends in nearly all of his friends ending up in critical care, he learns from his mistakes and better plans for problems. He even takes on a member of the Akatsuki alone - Hidan - and defeats him.
Asuma
Asuma is the person who inspires Shikamaru to be braver, so it's only fitting he land amongst the bravest as well. Initially, Asuma seems so confident in his own skills that it's easy to write off his attitude in the field as just that, confidence, not bravery.
The audience, however, eventually sees the truth about Shikamaru's sensei. He is confident in his abilities, but he also doesn't fight for himself. Asuma is ready to say goodbye every time he steps into a fight. He does everything in his power to protect his students from death, taking the worst of a fight himself. Asuma gives his own life so that the next generation can become even better than him, a philosophy he passes on to Shikamaru.
Naruto
Naruto is certainly one of the bravest in the series, but he grows into that bravery. Early in the franchise, his insistence on taking on opponents stronger than him, or even standing in the middle of a battle and refusing to fight at all, is born more out of his own lack of experience than it is bravery.
Because Naruto is so open and friendly, he just assumes everyone is like him and deserves a chance to make a friend or get a second chance. He's not entirely aware of the reality that some of the people he tries to talk down from a fight are still going to try to kill him until they're already taking aim. As he becomes older, he certainly realizes that, but there are still a lot of characters braver than him.
Jiraiya
Jiraiya doesn't seem like the kind of shinobi who takes anything seriously. He spends his money on drinks and women - and also spends the money of his students. It's important to remember, however, that while most shinobi work in teams, Jiraiya spends most of his adult life working alone and in potential enemy territory.
He spends most of his time traveling under the guise of working on his novels. Sure, he writes a few novels in his career, but his time is truly devoted to infiltrating enemy territory and bringing information back to Konohagakure. He knows how dangerous the job is, but that doesn't stop him from investigating potential enemies alone, which also eventually leads to his death when he faces off against his former student, Pain.
Lee
Rock Lee is easily one of the best hand-to-hand combatants in the series. He never misses a chance to train, turning hanging out with friends into contests of strength, which makes him a formidable opponent. He doesn't, however, have any jutsu of his own. He can't create shadow clones or walk on water or any of the things shinobi learn in school.
He knows from a young age that he won't ever have the same level of power as his classmates, but that doesn't stop him from training. It also doesn't stop him from going out on missions alone to rescue his friends. He understands the risks of going up against a shinobi with more raw power than him, but he does it anyway.
Itachi
Of all the characters in Naruto, Itachi Uchiha has one of the strangest character arcs. The audience spends much of their time believing him to be a villain since he was behind massacring his entire clan other than his younger brother. The truth is that massacre was all part of a larger plan to protect his little brother.
Itachi spends a decade with villains whose causes he doesn't believe in, working alongside them, always with his own hidden agenda. He's not the most powerful of them all, despite his Uchiha bloodline, and his life is an incredibly risky one since his entire village thinks he's a villain as well. Itachi shows immense bravery in trying to continue to protect his little brother and his village from afar despite the target on his back.
Kakashi
Kakashi is one of the few teachers in the series who gets a whole lot of backstory. The audience gets to learn a lot more about his character through flashbacks. As a child, he's a prodigy and an incredibly cocky fighter. His fighting on his own is born from overconfidence then, not bravery. It's as he gets older and realizes the value of teamwork and the reality of heartbreak that he's truly brave.
Kakashi becomes a teacher despite his desire to keep his distance from everyone in Konoha. He grows to care for his students, putting himself between them and harm's way. He even faces off against Madara Uchiha, despite being sure he won't survive the fight.
Hinata
Hinata is such an underrated shinobi. She's often dismissed because of her shyness and her gentleness by her peers. What they tend to overlook, however, is just how committed she is to becoming a valued shinobi in her community. She's constantly told that she's not tough enough or not good enough, but that doesn't stop her. Hinata works incredibly hard to be on the same level of most of her classmates.
Hinata also stands her ground, much like Rock Lee, in the face of more powerful opponents. Though she knows that she's not a match for someone like Pain, Hinata is initially the only one in the village to come to Naruto's defense. Hinata constantly puts herself between others and their enemies in an effort to protect them, or even just buy them a little time. That's incredibly brave of her.
Choji
Like Hinata, Choji is very underrated. His peers don't think he's as smart as his teammates, and he's definitely a little more fun-loving than they are. Even Ino tends to dismiss him as nothing more than a teenage boy who pays more attention to food than he does to her and Shikamaru. Choji's love for food, however, directly correlates to his size-change jutsu and his skills as a shinobi.
Choji first shows just how brave he is when he volunteers to stay behind on the Sasuke Recovery Mission so that the rest of the team can go on. Shikamaru warns Choji against the different moves that could harm him, but Choji pushes on to protect his friends anyway. He's also the one member of his team who is able to stand up to the reanimated corpse of Asuma, taking on their old sensei with the full extent of his power.
Guy
If anyone in the audience wondered where Rock Lee got his particular brand of bravery from, they need look no farther than his sensei Might Guy. Like Lee, Guy doesn't have access to the same types of abilities as most shinobi, but also like Lee, he doesn't back down from a fight.
Guy is the one who stands up to Madara Uchiha with Kakashi. He opens the final gate of his abilities, despite knowing that it could kill him. He's willing to sacrifice himself so the rest of the shinobi world could go on.