The fact that a human learns the powers at all. The shock shown by the Strangers upon learning this is a fantastic moment in the film.
Dr. Schreber gets one at the end. Schreber is the human assisting the psychokinetic aliens by injecting fresh memories into each person in the city each night. When he finds John, the human who has just discovered similar powers, the aliens capture John and ask Schreber to inject John with their collective memories. He instead injects John with a lifetime of memories of being taught by Schreber how to hone his psychokinesis, resulting in...
John's fight against The Strangers at the end of the movie definitely counts as one. I still get a chill whenever the table rocks forward and his eyes pop open and it doesn't go away until the end of the fight scene.
Trevor Jones' score is awesome throughout the whole movie, but it reaches apocalyptic heights in this fight. With everything breaking up around John and the Strangers as they battle combined with the rousing music, it almost resembles Ragnarok in its grandeur.