Avatar: The Last Airbender definitely redefined the way animated kid shows were made. It was more serious with a lot of worldbuilding and important social questions integrated into the storyline seamlessly to create commentary that wasn't forced in the smallest bit.
But by far one of its more important features is the abundance of well-written characters like its title protagonist Aang. In fact, his relationships with friends, his approach to different situations, and all the small details are what make him such a complicated person to read and put in a Hogwarts house.
Not Hufflepuff: "If I Try, I Fail. If I Don't Try, I'm Never Going To Get It."
To become the Avatar, Aang needs to master all for elements. But he can't do it without the help of benders who could teach him because he can't learn it all on his own.
The problem is that it's not easy, and a particularly difficult element for Aang was fire. Aang could have given up, but he realized that he should try again and again before he manages to learn what he needs to learn. This clever realization could show that he is a Ravenclaw.
Hufflepuff: "Will You Go Penguin Sledding With Me?"
When Katara and Sokka discovered Aang in the ice, they didn't immediately realize who he was. He seemed quite childish which was appropriate for his age, but Katara could feel there was something more to him.
But this childishness and fun-loving nature are carried by Aang throughout the show. This could mean that he is, in fact, a Hufflepuff.
Not Hufflepuff: "Aang: This Is Exactly Why I Didn't Want You To Come. It's Too Dangerous! / Katara: And That's Exactly Why We're Here."
But even though Aang likes to joke around and play games, he can actually be very serious and focused on the matter at hand allowing him to do his job as the Avatar.
Likewise, he isn't afraid to protect those he loves and to engage in a fight when necessary (though he does believe in using more peaceful means to resolve conflicts). This bravery could signal that he is a Gryffindor.
Hufflepuff: "Let Your Anger Out, And Then Let It Go. Forgive Him.
Aang is an incredibly peaceful person who always tries to find a way to settle a disagreement. He is against murder or war which is why he even spares the Fire Lord at the end of the show.
This friendly and peaceful approach to everything also prompts him to encourage Katara to forgive the man who killed her mother. This could show Aang's Hufflepuff nature.
Not Hufflepuff: "The Past Can Be A Great Teacher."
Though Aang is only twelve years old (one hundred twelve if you count the time he spent in the ice), he is very intelligent and even wise for his age largely thanks to the monks who taught him.
This is why Aang realizes that the past, no matter how terrible, can be a very good teacher and can help prevent the same mistakes from happening - a truly Ravenclaw judgment.
Hufflepuff: "This Isn't About Finding A Teacher. This Is About Finding My Friend."
When Team Avatar is looking for an Earthbending teacher for Aang, they remember about his old friend Bumi who they had met earlier. Returning to the Earth Kingdom city where Bumi rules, they realize that it's about to be taken over by the Fire Nation.
Yet, Aang wants to get in and find Bumi nonetheless. Not just because he needs a teacher but because he cares about his friend. This caring and protective side of him is clearly that of a Hufflepuff.
Not Hufflepuff: "I Was In The Avatar State... But I Was Outside My Body Watching Myself. It Was Scary. I Was Scary..."
The Avatar State is one of those things Aang can't fully control no matter how much he learns about it. And that's why he's so afraid of entering the state in fear that he will bring too much harm.
And that's what he confesses to his friends, probably one of his greatest fears of all. This openness to his darker side could show that he is an example of a good Slytherin.
Hufflepuff: "It's Easy To Do Nothing, It's Hard To Forgive."
Though Aang does want to spread peace and non-violence, he realizes just how hard it may be to become a forgiving person who does good as a response to evil.
He also acknowledges just how terrible inaction can be. All of these approaches to what it means to be a good person can show that he is a Hufflepuff.
Not Hufflepuff: "Katara: Aang, Stop! We're Not Allowed To Go Near It. The Ship Could Be Booby-Trapped. / Aang: If You Want To Be A Bender, You Have To Let Go Of Fear."
Sometimes, Aang makes mistakes. To an extent, this is due to his naivety and childishness, but his fearless nature also contributes to it a ton.
That's exactly why he persuaded Katara to go to the Fire Nation ship which helped Zuko find him. For some reason, Aang decided this was the best moment to say some wise words about bending which incidentally could make him either a brave Gryffindor or a smart Ravenclaw.
Hufflepuff: "Katara: Why Didn't You Tell Us You Were The Avatar? / Aang: Because... I Never Wanted To Be."
One of the most important features of Hufflepuffs is their selflessness. They don't want to be better than others - they just want to be happy and make others happy.
That's why Aang is so reluctant to take on the responsibilities of the Avatar. He never wanted to be one in the first place, yet he realizes that he needs to become the Avatar to restore peace in the world.