My personal favorites were:

When Zuko and Aang train and fight.

What Zuko said to Aang "I know you're scared and i know you're not ready to save the world, but if you don't defeat the Fire lord before the Comet comes there won't be a world to save anymore."

When Zuko and Iroh reunite in the tent.

The entire Agni Ki scene. (The music was amazing)

Of course the battle between Aang and Ozi.

And when everyone is in Ba Sing Se together and Aang and Katara Kiss.

What did YOU like about the epic series finale to possibly the best show ever made?