Waterbending is the only bending skill that was not learned from an animal. Waterbenders are said to have learned from the moon; in contrast, earthbenders learned from the badger-moles, airbenders learned from the sky bison, and firebenders learned from the dragons. The entire concept is awfully similar to animal-based martial arts in Real Life, made famous by Hongkong martial arts movies like Jackie Chan's Snake in the Eagle's Shadow or Tiger and Crane Styles (best known for being edited into Kung Pow! Enter the Fist).
As mentioned on the main page, the bending styles themselves are based on actual Chinese martial arts (Waterbending is Tai Chi, Earthbending is Hung Gar, Firebending is Northern Shaolin Kung Fu, Airbending is Ba Gua). Exceptions not covered are:
Toph's own Earthbending style, taught directly by the badger-moles, is actually based on Southern Mantis style
Metalbending, based on Xing Yi Quan, which quite appropriately was developed in captivity as well
Bloodbending, based on Qin Na Shou, which was also quite appropriately a grapple-based technique
Redirecting lightning is the only style taken from a sword technique, the obscure Tai Chi sword discipline, which is appropriate given that Iroh created the technique by watching waterbenders.
Even better is that all of the above are unique martial arts styles compared to the respective culture's norms, because they are all unique to a certain character or (in the case of Lightning redirection and Bloodbending) a very small group.
Extra points for Lightning redirection being explicitly based on Waterbending techniques.
You can probably catch some differences between Katara and Pakku's waterbending styles, since Southern and Northern are legitimate Tai Chi variants.
"Katara" means "curse" (both as in "hex" and "swear") in Greek. Of course, this is just a weird coincidence, but it is too odd to not mention. One would suspect that the character was so named because a Katar is a type of Indian dagger, though.
Although the earthbender was Toph's original design, but when her design was changed, that design inspired later characters The Boulder, Sud (Roku's earthbending teacher) and "The Ember Island Players"' Toph (directly taken from that design).
Some argue that the airbender in the opening is Monk Gyatso. Others claim it's an older Aang (a theory largely debunked by the confirmed older Aang in the opening to The Legend of Korra, who looks much different), and still others suggest it might be one of the unamed monks from "The Storm".
Before voicing Avatar Roku, James Garrett had previously worked as an announcer for movie trailers (most famously the Harry Potter films). Rather appropriate for a character whose primary role in the story is to inform everyone of a dramatic event happening THIS SUMMER.
Actor Existence Limbo: After Mako's death, Iroh was relegated to only two silent appearances for the first half of season 3, before Greg Baldwin was introduced as his new voice.
While this was averted in the original version as Aang was voiced by a boy, it was played straight in Russia, the Philippines, Japan, Korea and Taiwan.
Not used in the show itself (12-year-old Aang is voiced by Zach Tyler Eisen), but Lampshaded in the play in The Ember Island Players, where Aang is played by a (visibly adult) woman (voiced by Rachel Dratch).
This doubles as a reference to Peter Pan, where the eponymous eternal child is traditionally played by a petite woman rather than a prepubescent boy.
Dawson Casting: Aversion: Aang and Toph are voiced by actors of about the correct age. The actors who play Katara and Sokka are not much older than their characters, either.
Played straight with Suki, whose voice actor Jennie Kwan was in her 30s.
Played straight in Chile with Aang, whose male voice actor (René Pinochet) was almost 30! Justified that he was born prematurely and his voice hadn't changed much since childhood. Dante Basco, the actor for Zuko, also had a young voice in his late 20s when he did voice work for the show.
Fan Community Nicknames: Due primarily to one certain "megafan"'s infamous, longrunning satire comic of the Avatar fandom, fans have come to almost unanimously accept the term "Avatards". (Some people feel that, in referring to the term "retard", fans' use of this label is demeaning to the mentally-disabled. The creator of the comics has also openly admitted to regret the choice of the word in retrospect.)
The term fell out of use after The Legend of Korra was announced, at least partially because of the Unfortunate Implications - it's now rarer to find someone in the fandom who calls themselves an Avatard than someone who doesn't.
No Export for You: Such an Animesque series seems like a shoe-in for a Japanese release, right? The first season was dubbed and advertised, but never officially released in Japan due to network failure.
The Other Darrin: Iroh was voiced by Mako Iwamatsu in the first two seasons, but his death caused Greg Baldwin to voice him in season 3.
Sokka's humor and mannerisms were derived from the improvisations of his comedian voice actor.
Additionally, in the episode "The Ember Island Players" the entire show was parodied hilariously by a play. The actor parodying Sokka wasn't funny enough and so Sokka tried to fix it by substituting his own jokes with even more hilarious results.
Trolling Creator: Bryke, from time to time, took quite a few potshots at the Zutara shippers. The Ember Island Players episode openly mocked the cliches typically associated with Zutara fanfics. Then there was Book 4: Air, a video openly mocking how incompatible the two would be as a couple.
"Laogai" is actually a phrase referring to reformative training, usually associated with Communist China.
The background music in Earth Kingdom dinner scenes ('The Blind Bandit' and 'City of Walls and Secrets') is an actual traditional Chinese tune called 'Mo Li Hua' or Jasmine Flower.
From the end of "Avatar Day": fried dough sticks to represent hated historical figures do exist.note You can see the Landlord bumming some off of Donut early in Kung Fu Hustle. Long story short, Evil Chancellor Qin Hui set up the Emperor's most loyal general Yue Fei as a traitor, leading to his execution before the truth was out. The fried dough sticks are always made in pairs to represent Qin and his wife.
Energybending in the Grand Finale becomes less of an Ass Pull if you're familiar with Chinese martial arts fiction, which commonly used "the removal of his martial arts" (via crippling nonfatal injury) as a Fate Worse Than Death for villains. Another common trope from this genre is having your villain driven insane with his own growing abilities... which might explain Azula (or Bumi, but he was always a little odd).
In a similar vein, Metalbending. Toph is shown using two different martial arts styles for standard (Hung Gar) and her self-developed (Mantis) Earthbending; Metalbending comes from a third style, Xing Yi Quan, developed in captivity just like Toph's metalbending was. note Jet Li uses this style in The One, when he bashes the prison walls just like Toph does, while his good counterpart uses a different style, Eight Trigrams Palm, same as Aang.
And blood-bending is based on Qin Na Shou, an appropriately grapple-based technique.
Toph was originally conceived as a guy. When designing the show's lead Earthbender, who was originally supposed to be a teenage boy, head writer Aaron Ehasz joked that it would be funny to see a small little girl take out all those big, burly Earthbenders. Though the idea was rejected by series co-creator Bryan Konietzko, the team still decided to work around it, and several discussions and redesigns later, Toph was born (and ironically became one of Bryan's favorite characters). Variants of her original character model makes a few appearances throughout the series in bit roles, most notably as a bender in the show's opening sequence (Roku's Earthbending teacher) and THE BOULDER!
Word of God says that the screechy actor who played her in the play is a flanderized version of her original character design. Aspects of her original male visual design and characterization were later incorporated into Bolin.
Speaking of THE BOULDER, the creators originally wanted him to be voiced by the Rock.
Incidentally, Azula was also originally conceived as a guy. Ty Lee and Mai did not even exist in the older drafts for the series.
In the season 2 premiere, originally Azula was going to vaporize her captain for letting it slip that Zuko and Iroh were prisoners, but realized they couldn't do that on a kid's show.
Zuko was originally going to find his mom. See also Cliffhanger on the main page. The production staff even planned a storyboard for it and everything.
In the Avatar Extras for part one of the Season 1 finale, it is mentioned that there was an idea kicked around for a special about Iroh's failed attack on Ba Sing Se, but it never took off.
A dropped subplot revolved around Momo being the reincarnation of Aang's mentor, Monk Gyatso.
The identity of Aang's parents was going to revealed but this was later dropped.
There was going to be an episode that involved Aang and Sokka getting handcuffed together.
Originally, in Book Three, Azula was apparently meant to have been in an arranged marriage, and Appa, in the season finale, would have been confirmed as female. They decided not to do this, for obvious reasons.
According to the I.P. Bible, Aang and Katara were not supposed to end up together. Aang's crush on Katara was to remain one-sided until the end. Katara actually had more Ship Tease with the then male!Toph than Aang, but nobody was going to end up in a relationship. While the show was in production, Bryke decided to have Katara/Aang happen as they came to adore Aang and realized that Kataang was their "soft spot".
Aaron Ehasz, the head writer has told many people (even providing a lecture at UCB) about how there were originally four seasons of Avatar drafted but it was cut down to three after Shyamalan was given rights to create a movie trilogy. He also mentioned wanting Zuko and Katara to end up together. Episode writer Joshua Hamilton has confirmed twice that Zuko/Katara was toyed with in Avatar Extras. Jae-Myung Yoo, the animation director drew a poster featuring Zuko and Katara together as a homage to Ehasz's plans. Shyamalan has also stated that Bryke had no idea who Katara was supposed to end up with when he talked to them privately. This is in direct contrast to Bryke's interviews that the Zuko/Katara ship was never a possibility and that three seasons was always the plan, although the two have a history of trolling and lying.
The writers originally intended to have Pong living with another character named Ping for comical reasons, but they decided otherwise as it was "not funny enough to put in the episode". In the DVD commentary for "City of Walls and Secrets", the creators revealed that they had initially intended for Pong to have a much larger comical role that would stretch to the end of the season, but that he got edited out in subsequent revisions. Word of God said he kept getting cut from the scripts and by the end of Book 2 they completely forgotten about him.