I.ii. Ghost Stories - Tennant (2009)

Hamlet hears steps behind him, quickly wipes a tear and walks off camera as Horatio and the soldiers walk in. As soon as he sees who it is, we get an excited embrace. The soldiers remain at attention in the background. The staging contrasts an intimate friendship and the more hierarchical relationship between prince and soldiers and so gives us a Horatio that is closer to Hamlet than in some versions. I've spoken before of the divide that exists between the two friends, but here we get the feeling Hamlet sees Horatio as an equal.

The soldiers may well fear that admitting to seeing a ghost could lead to reprisals, which is a reasonable motivation for them to go to Horatio first. In this scene, they let him take the lead and tell THEIR story. Marcellus only jumps in when Horatio hesitates (showing he doesn't know Elsinore very well, he needs prompting as to what the location is called).
Without Horatio finding the right details to convince Hamlet, would the prince have believed this story? It's all about trust. Horatio, after all, is an educated man like he is, one not prone to superstition. Horatio has trouble bringing himself to tell the story, because it doesn't fit his/their world view. This version plays it very much like Horatio at first chickens out. "I saw him... once." He has to steel himself to finally say he saw him yesternight.

As for Hamlet, Tennant continues to play the grief as waves of sadness that sometimes assail the character, his voice breaking in points, but on an even keel otherwise. In my experience, that's exactly what grief is like. His body language changes with the talk of the ghost. He crosses his arms, a barrier of doubt between himself and the other characters. Though he tests them at first, especially the soldiers' loyalty (perhaps thinking Horatio is their dupe), he soon believes.

Cuts
There are a number of small cuts in this scene, a line here and there. One's line's absence in particular revealed something about the text. "Would I had met my dearest foe in heaven / Or ever I had seen that day, Horatio!" is cut. Usually, it comes just before "My father!--methinks I see my father". There is a dramatic irony here, as Hamlet mentions in succession heaven and his father. One line may inspire the other, but Hamlet is about to find out that his father is actually in hell. Later, he'll be unable to kill the praying Claudius from fear he would send him to heaven, which indeed would have sent his dearest foe there. Heaven and hell, another mirrored reflection in the play, and the two brothers each on the wrong side.