The Waving Flag
After Neil Armstrong and Buzz Aldrin planted the American flag on the moon it appeared to wave or flap around in a breeze. As the moon has no atmosphere there would be no breeze to make the flag move, so many conspiracy believers use this to support their belief that we didn't actually land on the moon. The truth of the matter is that because the two astronauts had trouble planting the flag, when they did manage to make it secure it was swinging around a lot. This would make it look like the flag was ‘waving in the breeze’.