Daniel breaking the sheets of ice in the second movie.
Made all the more awesome when Mr. Miyagi comes in and it seems like he's going to bail Daniel out. He is told that the odds are 3 to 1 that Daniel can't do it... and promptly bets six hundred dollars that he can.
Also from the second film, Daniel and Miyagi saving a few villagers, Sato and the bell girl when the typhoon hits.
The final showdown between Daniel and Chozen. As Miyagi puts it: "This not tournament, this is real!" Daniel could have gotten killed and he knew it. He still didn't back out.
The crane kick was originally a Moment of Awesome but due to Memetic Mutation it has become comical.
The final fight scene. Under injuries that would put a lesser teenager down and out, Daniel returns to the mat and dances around on his injured leg to get two points on Johnny before the Cobra Kai gets one on him. Then, even after Johnny has viciously targeted his previous knee injury, he remains in the fight. And YMMV on the Crane Kick. When Daniel executes a perfect one and wins the tournament, it is one of the most triumphant moments in 80s film.