Evidence 1
I was wondering about some of the past works the creators have been apart of, so I went researching. This is what I found on Michael Dante Dimartino:
I have found some interesting things on Michael. He was the director of a show called Atomic Love and it's about a girl and a robot falling in love. Uh, totally opposites huh? And then he was the assistant director of King of the Hill, which I don't watch, but one user commented it as "The Yin to the Simpsons' Yang". So to me, this shows that he is into the opposites/Yin-Yang thing, even if it's somewhat minor.
Evidence 2
In The Avatar Returns, Zuko seems to be watching Katara, which could mean he is drawn by her, possibly because this is their first encounter.
Evidence 3
In The Waterbending Scroll, he is fairly nice to Katara. We have seen him act around Sokka and Aang, and he is not gentle and nice to them. He yells and makes demands without a second thought, whereas with Katara, he acted differently.
Evidence 4
In The Fortuneteller, Aunt Wu said Katara would marry a powerful bender. She also saw no love in Aang's future and she used the most reliable method of fortuntelling on Aang. Later we find out that Katara realizes Aang is a powerful because of Sokka's comment (thanks Sokka) and shes acts astonished. This is proof she didn't feel about him that way, but we know she has thought of it now. This could also be foreshadowing.
Evidence 5
In Bato of the Water Tribe, Jun said Katara was Zuko's girlfriend three times and Zuko didn't deny it once. He also kept Katara's necklace around his wrist, the entire time. And when Aang gave Katara her necklace back, she asked to give Zuko a kiss, even though she was being slightly sarcastic. This still could be foreshadowing.
Evidence 6
In The Chase, Iroh says, "It's ok to let those who love you help you." Later, Katara says, "Zuko, I can help you." Neither Katara or Zuko knew what Iroh had said. Perhaps this is a Zutara farshadowing. Also it shows that Katara sees Zuko as a person too. It proves that she does know he exists, and has problems like the rest of them. She doesn't think of him as the "enemy" anymore, otherwise she wouldn't have offered him her help.
Evidence 7
In Bitter Work, when Iroh mentions the waterbending, Zuko smiles as if he was remembering something (or someone)...It easily could have been Katara, considering he's had numerous encounters with her, and kept her necklace for a good amount of time. And we know it wasn't stashed away, as he had it handy in his sleeve when he met Jun.
Evidence 8
The newest hope and speculation is about Zuko joining the Gaang. He, in a sense, is starting to realize where is life it going. He is realizing, with the help of Iroh, and Azula surprisingly, that Ozai does not want him back. He won't accept it, but he knows it. Also, by him chopping that hair off, he is showing that he grasps his fate, and that he is now a fugitive of the place he was/is so desperately trying to retain. So, as a result, when more episodes wear on, he could run into the Gaang, and maye something else like when Azula told him that Ozai thought he was a disgrace could happen, making him want to join them, or maybe just consider it. And then what? If he joins, we judge him to be very unsocial, maybe a little hesitant at first. But that will go away once he's used to them, and then that's when the Zutara relationship can blossom.
Evidence 9 (Symbolism)
There is a large banner with Zuko looking at the sunset right after he found Katara's necklace on a certain site that made me think of this. While I was looking at it I realized that while he was looking at the sunset he was holding her necklace in his hand. Usually when someone looks at the sunset they're in a daze, or very happy. And when you're like that and looking at the sun and the beautiful colors that it casts in the sky don't you think of the future? I know I do. So that got me thinking...he's looking at the sunset with Katara's necklace in his hand...he might not have been thinking of the future (though I think he was). He was probably thinking of how many useful ways he could take advantage of his new find. Which is in the future. So to me that means Zutara will happen in the future.
Evidence 10 (Yet more Symbolism)
In The Earth King, Zuko was gasping for water during his fever. This is a small strand of symbolism, but it is representative of something.
Evidence 11
In the preview of the upcoming Season 2 Finale, we see Zuko and Katara in a cave. Katara confesses the loss of her mother, and Zuko reacts, calmly. We then see Katara holding the vial of special healing water in her left hand, while approaching Zuko's scar with her right. When Song tried to touch the scar, Zuko stopped her, but he doesn't seem to be holding any resistance to Katara. He could also be apologetic to her for turning away her offer of help the last time they saw each other, in The Chase.
Update: So the season finale didn't quite turn out as we had expected. Still, Katara knows that Zuko has personally suffered from the war as well, and there is at least a small glimmer of hope that she can forgive him for his betrayal, and help him to become someone better.
