Let’s just take a brief look at the progression of Aang’s crush on Katara throughout the whole series - it’s really touching to see how it evolves from an innocent childish crush to the deepest level of care and love:
-Thought she was attractive when he first met her (”The Boy in the Iceberg”)
-Superficially tries to impress her with an airbending marble trick (”The Warriors of Kyoshi”)
-Really starts getting infatuated with her (”The Fortuneteller”)
-Risks his life to make sure Katara is safe from falling debris (”The Cave of Two Lovers”)
-Chooses Katara over pure cosmic energy and also openly admits he loves her (”The Guru”)
-We start to see some hints of Aang’s feelings being reciprocated (”The Headband”)
-Gains the confidence to finally directly reveal his feelings for Katara (”The Day of Black Sun, Part 1″)
-Both communicate their feelings for each other but the future of their relationship is uncertain (”The Ember Island Players”)
-But they ultimately end up together in a really deep mutual love :) (”Sozin’s Comet, Part 4″)