Air Nomads might have been wiped out and so may have the sky bison. A significant amount of tradition and culture was lost.
The Southern Water Tribe was heavily impacted by the war, since most of their original benders were taken and imprisoned until death. This caused the Southern Tribe to extremely deteriorate, and many of their traditions were nearly wiped out. Of course the help from their sister tribe will presumably lighten those issues. On the same note, the original moon spirit of Tui was killed by General Zhao, but was replaced by Yue soon enough. This meant the death of the Tribal Princess.
Many Earth Kingdom cities like Taku, were completely destroyed and abandoned. Towns, such as Jet's, were completely destroyed.
Of course many soldiers and people died during the war, such as Kya (Katara's mother) and Lu Ten (Iroh's son).