The part in Act III, scene ii, when Hamlet expresses just how much Horatio means to him.
Hamlet: Give me that man That is not passion's slave, and I will wear him In my heart's core, ay, in my heart of heart, As I do thee.
In the Kenneth Branagh version, Claudius has a white-hot anger rant after he finds out about Polonius's death. Just when he seems beyond the point of no return as far as rage and madness goes, he suddenly collapses into Gertrude's arms like a child seeking protection. It's a truly vulnerable, human moment of real fear and love in sharp contrast with the "villain" he's supposed to be.