When reformed Azula meets Appa. She caresses his fur and seems to approach the idea of a Sky Bison with childlike wonder; Appa, meanwhile, just looks at her with his huge, curious eyes.
Sokka reading to Azula in the gardens, seemingly beginning to forgive her for the horrible things she did to him and the others in the series. They look so happy together...
The children of all the living protagonists playing together in peace in the epilogue. It's not just a happy ending for the main cast, but also a symbol and microcosm of the new order of peace and harmony that has followed on the war in the original series.
Now I have a beautiful daughter who will rule the Water Tribes one day, with the love and wisdom my family and friends have shown me. I have been brought back to life, and life has shown me that all things are possible.