Just as an interesting thought experiment, I was thinking about which of the six abilities would be used to set the save DCs and attack bonuses for the bending from the Avatar: The Last Airbender television programme and related media. What do you think?

Well, if we're sticking with the idea that it's basically a form of martial arts, so benders would probably be some form of monk. A monk's Ki-save is based on their WIS score, since that's the score meant to represent your physical awareness and senses.

Depends on the element. I'd say Constitution or Strength for earth, Wisdom or Dexterity for water, Strength or Charisma for fire, and Dexterity for air.

If you base it on the t.v show then  i think it  depends on the specific bending move as they are extensions of characters actions or beliefs. Something like bending some ones spirit would likely be charisma while, generating lightning is likely intelligence  and redirecting it is wisdom.  I think an approach where different bending moves have different checks associated with them would make the most sense. 

Dexterity because you do stuff with your hands.

Avatar seems to mostly be based on your "Oneness with the Elements" for the bending which would make it Wisdom [ you can describe druid spellcasting as their "Oneness with nature" and cleric spellcasting as their "Oneness with divinity" ]. However, if I remember correctly, there is a degree of innate ability to it so it could be Charisma like a Sorcerer, but Wisdom seems a much more intuitive fit to me.

Quote from Solarsyphon >>

If you base it on the t.v show then  i think it  depends on the specific bending move as they are extensions of characters actions or beliefs. Something like bending some ones spirit would likely be charisma while, generating lightning is likely intelligence  and redirecting it is wisdom.  I think an approach where different bending moves have different checks associated with them would make the most sense. 

 That is certainly an interesting proposition, but it seems very at odds with how D&D usually handles things. I think that lightning would simply use the same ability as Firebending, if only for simplicity's sake, so that players wouldn't have to generate a whole bunch of different save DCs and attack modifiers. If it did use something different, though, I'd imagine it using Wisdom, 'cause it seems that it's all about being aware of one's own ki; I don't see how it's intellectual. Though I do agree that Aang's Spiritbending seems like a contest of Charisma; or maybe Ozai just had to make a Charisma saving throw?

Anyways, I suppose that I might as well elaborate my own thoughts on the matter:

Judging by characters like the Boulder, it does seem like there's some sort of correlation betwixt physical Strength and Earthbending ability; then again, correlation doesn't imply causation, and there are plenty of Earthbenders (e.g., Long Feng) who don't appear physically strong.

I do think that Dexterity makes quite a bit of sense; it often seems that one's ability to make the physical martial art motions dictates one's bending ability (Amon notwithstanding).

Iroh talks about how Firebending comes from the breath in Season 1, so that might make a case for using Constitution.

Intelligence seems right out; I don't think that bending has much of an intellectual component, besides memorising the forms. (Then again, as an edge case, maybe Amon's special stuff is Intelligence-based, as it is described as "psychic." That or Charisma, probably.)

Wisdom could be justified; there is talk of, e.g. feeling the "push and pull" of water, and "waiting and listening" to the earth. Plus Wisdom is the "spirituality" ability, and bending often has to do with that.

The bit in Season 3 where Zuko talks about Firebending being powered by anger seems to imply that it could work with Charisma.