I think that many of the minor characters in the original series don't get enough screentime as they deserve. Some of them have so much potential and background to be filled in! I like the idea of taking a minor character and giving them a life and a more rounded personality.
For example, Jin was a girl that met Zuko in Ba Sing Se and took a liking to him. Who was she really? Why did she like him? Did she wonder about his scar at all? Similarly, what did Song think after Zuko stole her ostrich horse? What's the story behind her scar?
Going in a different direction, one fanon I was reading was about Shoji, the boy that become friends with Aang (as Kuzon) and saw him earthbending at the end of episode The Headband. It was cool because the fanon told the story of what Shoji did after seeing the earthbending.
There is also a fanon documenting the story of the Freedom Fighters. I haven't seen one about the Yuyan Archers, who I think are pretty awesome. I think I may write a fanon series that develops these minor characters into more interesting people.
What are your thoughts? Which minor characters do you like a lot?