There have been very few shows that have resonated with so many different demographics of people as much as Avatar: The Last Airbender has. The American-Anime style kids-show was incredibly mature. thought-provoking, and was truly a series that was for everyone, not just kids.
The series introduced the world to the memorable characters of Aang, Katara, Sokka, Appa, Momo, Zuko, Iroh, and many, many more all over the course of just 61 total episodes spanning 3 seasons. However, none of those seasons would have happened if it hadn't been for the universal success of the first one.
The King of Omashu, Episode 5 (8.2)
During this episode, the main trio thinks that they're going to be making a quick pit-stop at the Earth Kingdom city of Omashu so that Aang can show Katara and Sokka the world's biggest super-slide... only for Aang's identity as the Avatar to be revealed, causing the group to be imprisoned. The King of Omashu then puts Aang through a series of three rigorous tests (all of which Aang manages to pass) but then says that Aang must also guess what his name is. After some thought about the tasks he had to undergo, Aang makes the realization that the king is none other than his old-friend, Bumi (still rocking it at 112 years old).
The Avatar Returns, Episode 2 (8.3)
After Aang emerged from the iceberg and started to get acquainted with the southern water tribe in the pilot, the following episode dealt with Prince Zuko showing up at the south pole looking for the Avatar. Aang eventually gives himself up when Zuko promises to leave everybody else alone, prompting Katara and Sokka (and Appa) to head after the war-ship to save Aang. As it turned out, the Avatar didn't need much help being saved as Aang enters the Avatar State for the first time and shows the Fire Nation exactly why he is a force to be reckoned with.
The Southern Air Temple, Episode 3 (8.5)
The main trio escaped Zuko's grasp and made the decision to head to the North Pole to find a waterbender to teach Aang and Katara, but their world-wide trip had plenty of pit-stops on the way - the very first one was Aang's old home, the Southern Air Temple. Sadly, after being untouched for 100 years, the temple is vacant, dusty, and serves mainly as a tomb to the airbenders that had lived there, including Aang's old mentor, Monk Gyatso.
Some good news does occur during this episode when the group finds Momo and adds them to their little gang, as well as the introduction of Captain Zhao and the proper butt-kicking that Zuko handed him.
The Deserter, Episode 16 (8.5)
Aang tried tampering with the natural balance of the Avatar Cycle when he attempted to learn firebending (before mastering water and earth) during this episode. When the group hears about a Fire Nation deserter who lives in a nearby forest, Aang insists on finding the man and learning from him. Sadly, upon finding the firebending master, Aang is only concerned with the power that he can possess with fire and doesn't consider it's deadly possibilities. As a result, Aang accidentally burns Katara and develops a phobia of firebending that lasted for the majority of the series. However, because of Aang burning her, Katara discovers that she has healing abilities with her waterbending.
The Waterbending Master, Episode 18 (8.6)
After an entire season of trying to find a waterbending teacher, fans knew it wasn't going to be that simple. The main trio finally arrive at the North Pole and find a waterbending master at the Northern Water Tribe... only for the sexist old-man to reveal that females are forbidden from learning waterbending and simply use their powers for healing. Furious, Katara challenges the master to a fight (holding her own incredibly well) but still ultimately ends up losing. It's then revealed that the master, Paku, was meant to marry Katara's grandmother before she fled south... causing Paku to reflect on his flawed-mindset and accept Katara as a pupil.
Avatar Roku: Winter Solstice, Part 2, Episode 8 (8.9)
The introduction of the Spirit World was a shocking revelation for fans, and things only got crazier when it was revealed that Aang could speak to his past life, Avatar Roku, during this episode. The trio travels to the Fire Nation, lands on an island that houses the Temple of the Avatar, and Aang manages to speak with Roku before the gang is captured by rogue fire-sages, Zuko, or Zhao. The main-storyline for the entire series is then revealed by Roku to Aang - he must master all four elements before Sozin's Comet arrives in the summer, or the Fire Nation will use its power to take over the entire world.
The Storm, Episode 12 (9.1)
While the Winter Solstice episodes may have told audiences what Aang was up against for the entire series, it was this episode that answered the question of how he ended up in the iceberg in the first place. Not only that but a parallel story fans also find out how Zuko got banished (as well as how he received his scar).
For Aang, it's revealed that he was going to be sent away from his home in order to train for the impending war - so he runs away on his own and gets trapped in a storm where the Avatar State froze him for safety. Meanwhile, in a shocking twist, it was revealed that Zuko received his scar from his own father and was banished for refusing to fight him.
The Blue Spirit, Episode 12 (9.1)
Another Zuko twist (this one was way cooler). When Katara and Sokka get sick, Aang ends up getting captured by Zhao and held captive in a massive Fire Nation prison. With the rest of the team incapacitated, Aang doesn't seem to have much hope - that is, until a blue-masked figure who wields duel-blades mysteriously arrives and helps free Aang from his imprisonment. Just as Aang and the anonymous savior are about to escape, the masked-man gets knocked-out by an arrow. Aang then takes off the mask and the Blue Spirit is revealed to be (gasp) Zuko, who Aang chooses to take with him as he continues to make his escape from Zhao.
The Siege of the North, Part 1, Episode 19 (9.4)
It was all leading up to this and it certainly delivered. While Aang and Katara had managed to find themselves a waterbending master, they had also managed to draw the Fire Nation (led by Admiral Zhao) straight to the Northern Water Tribe with about a hundred warships. Aang, as well as the Water Tribe Army, hold their own against the invaders for a day, but it's clear that they'll be outnumbered by daybreak. So, Aang travels to the most spiritual place in the North Pole in order to contact the spirits for their help... only for Zuko to show up and steal Aang's body once he enters the Spirit World.
The Siege of the North, Part 2, Episode 20 (9.7)
After Katara and Sokka rescue Aang from Zuko, Aang reveals (from the info he got in the Spirit World) that Zhao is going to try and kill the Moon Spirit. Unfortunately, Zhao succeeds in his fatal attempt and murders the koi fish which the Moon Spirit resided inside of, causing the moon to 'black-out' and take away the waterbenders powers completely. With all hope lost, Aang enters the Avatar State and merges his spirit with the Ocean Spirit, turning into a massive waterbending koi fish that absolutely decimates the Fire Nation forces within minutes. Meanwhile, Princess Yue (having been touched by the Moon Spirit as a baby) sacrifices her life in order to save the Moon. With the Fire Nation defeated and the Moon firmly back in place, Team Avatar concluded season 1 on quite the high-note.