Appa
Appa is Aang's flying bison and his spirit animal guide. It's also quite possible that Appa is the last living creature of his specie. He was with Aang when they fell into the ocean during a terrible storm 100 years ago, and Aang formed the iceberg that saved them both from drowning.

Appa transports Aang, Katara, Sokka, and Momo around the world in their quest to stop the war. He seems pretty content, but if he needs or wants something, he makes himself known. He comes on command when Aang blows on his bison whistle, which is at a frequency that only flying bisons can hear it. Appa has also proven himself to be quite the useful fighter. His large size and strength is intimidating enough, but by slamming his tail to the ground he can create a huge gust of wind that can blow a dozen men away. He also can be fiercely defensive if Aang is in trouble, and without warning will attack whoever is causing him harm.

Appa, as are most flying bisons, are very large and have long white fluffy fur with tannish arrows and stripes. They also have six legs, five stomaches, and weigh around 10 tons. Their diet contains mostly vegetation, as you can tell by their flat teeth. Flying Bisons naturally have airbending abilities, and are considered sacred by Air Nomads. It is said that Air Nomads first learned how to airbend from flying bisons, and even borrowed their arrow tattoo design.

Momo
Momo is a winged-lemur, a once plentiful (and mischievous) specie that lived with the Air Nomads and was often kept as pets. However since the war, it's believed that most if not all of the Air Nomads and their animals (winged-lemur, flying bison, etc) have died out.

Aang found Momo when he, Katara, and Sokka visited the Southern Air Temple, and is now his pet. Momo's name comes from the fruit it took from Sokka at the end of the episode when it joins the group. (Momo is Japanese for Peach)

As a winged-lemur, Momo has enhanced hearing and smelling, and can sense danger (or food) from far away. Despite the desolate appearance of the Southern Air Temple, for Momo to have still been there gives hope to Aang that his people are still alive.