Which gaps between seeing certain secondary characters in Hamlet lend themselves to the play?

For the most exciting stories, we want the juiciest material—gaps where the character is in a really different place before and after. What comes to mind for you?
Here's what my mind jumped to: when Ophelia goes crazy (maybe), when Ophelia drowns, when Laertes comes back from France, and when Horatio leaves Hamlet alone after the ghost.
Once you choose your gap, the way to fill it in is to ask a lot of questions. What would the character have been thinking right after the events of the first scene? What happened to them to prompt their behavior in the next scene?
Let's dig into each of these in a little more detail.
Ophelia devolves
Before her breakdown, we see Ophelia having a tough time of things. In Act III, Scene 1, she has that bizarre argument with Hamlet, who she thought loved her. He gets quite nasty. During the play in Act III, Scene 2, Hamlet crudely flirts with Ophelia before insulting her and laying his head in her lap. Talk about mixed signals.
Then Hamlet stabs Ophelia's father to death.
So what happens to Ophelia between Act III, Scene 2 and Act IV, Scene 5 when she enters acting like a madwoman? Her feelings about Hamlet and her father must have been rushing around her mind, changing constantly, tormenting her. Where does she go after the play ends? Does she talk to anyone? What were the exact circumstances of her "break"—when she started behaving irrationally?
Dig into Ophelia's specific actions. Why were folk songs on her mind? Do the lyrics she sings reflect some message she's trying to send, or some thought(s) she's been dwelling on? Do they reflect motifs you see elsewhere in the play—unfaithfulness, the difficulty of distinguishing true from false, the real nature of death? What motivated her to pass out the flowers? Who did she give them to, and why? (Some editions tell you whom Ophelia gives each flower to, but there is no definitive answer—in other words, you're free to make it up yourself.)
Think about this passage, spoken by the gentleman to Gertrude at the beginning of Act IV, Scene 5, explaining Ophelia's current state:

She says she hearsThere's tricks i' the world; and hems, and beats her heart;Spurns enviously at straws; speaks things in doubt,That carry but half sense: her speech is nothing,Yet the unshaped use of it doth moveThe hearers to collection; they aim at it,And botch the words up fit to their own thoughts;Which, as her winks, and nods, and gesturesyield them,Indeed would make one think there might be thought,Though nothing sure, yet much unhappily.

The emphasis is mine. There's some interesting stuff in there, no? You almost come away thinking she's not crazy—she's crazy like a fox. On the other hand. . . She hears that there are tricks in the world? Hears from whom? (For the record, she's also completely right.) Her unshaped words and gestures move listeners—if she's not shaping them, who is? Is she in touch with something deeper, some deeper truth, maybe, or some preternatural entity? Don't forget, there are ghosts in Hamlet's world.
As I watch Ophelia fly around the stage, yelling, insulting people, and otherwise behaving without the decorum required of a noblewoman, here's what I can't help wondering: Is she finally free?
Ophelia dies
One of the most provocative unanswered questions about Hamlet is about the nature of Ophelia's death. Was it suicide? The nature of her burial in Act V, Scene 1 suggests so, but Gertrude's description in Act IV, Scene 8 paints a more ambiguous picture. She kind of makes Ophelia seem like a girl playing in a stream who became overwhelmed.
Regardless of your opinion, though, there's more to this story. For one thing, how did Ophelia, who might not be in her right mind, manage to slip out of the castle alone? Were there no doctors or attendants around taking care of her? Was she abandoned? What drew her to the stream and the flowers? Do you think it might have something to do with beauty, or the difference between complex court life and simple nature? If so, how do those ideas form in her mind?
What does death mean to Ophelia? Does she seek it? Does she even understand the concept?
I'm not one for conspiracy theories, but there's one more question that has always bothered me: why did Gertrude watch Ophelia drown without trying to help her? If you look, Gertrude has the same character gap Ophelia does—after Act IV, Scene 5, we don't see her until she comes to report Ophelia's death.
Laertes revolts
When this play was new to me, I thought this scene was nuts. It came totally out of left field. The last time we saw Laertes, he was receiving advice from his dad before his trip to France (Act I, Scene 3). Soon afterward, we saw his dad asking Reynaldo to spy on him (Act II, Scene 1). Polonius thinks Laertes will be doing what many young men suddenyl given a lot of freedom do—drink, gamble, have sex, play tennis, get into sword fights. The next time we see Laertes is in Act IV, Scene 5, the same scene as Ophelia's breakdown. He's busting through the door to the throne room, roaring that he will have revenge, followed by an army shouting "Laertes shall be king!"
Well, okay. Maybe it's not quite an army, but Laertes definitely has a mob of commoners behind him. What happened? Laertes went from being a rich kid without a care in the world, off for a vacation full of debauchery, to a populist rabble-rouser brave and powerful enough to draw his sword on the king. What went through his head when he learned Polonius had been murdered? Was he scared to come back? What thoughts or feelings finally pushed him into coming back? How much grief was he actually feeling? How was he able to rally the commoners against Claudius? What was going through his head as he entered Elsinore castle, technically committing treason? Did he really think he would be king? Does he want to be king? If so, how long has he wanted to be king? Is he just using Polonius's death as a pretense to wage a rebellion he was already planning?
Horatio ponders
This is a more subtle story because the conflict is mostly in Horatio's head. Think about the state he must be in at the end of Act I, Scene 5. He sees a ghost, feels the earth quake beneath him, and sees his best friend act like a maniac. Hamlet asks Horatio and Marcellus multiple times to swear they will keep the ghost's secret, as if he's not really processing that they already have. Horatio says he's speaking "wild and whirling words," and that the night's events are "wondrous strange." Now, remember Horatio is one of the most easy-going, tolerant best friends ever. If even he is freaked out by Hamlet, things must be really intense.
We don't see Horatio again until he's spying on Claudius for Hamlet during the play (Act III, Scene 2). From this point on, Horatio is unfailingly faithful to his friend. Don't you think it would have taken a lot of soul-searching for Horatio to have decided to back Hamlet up? He's a scholar and rational thinker who is told, "There are more things in heaven and earth than are dreamt of in your philosophy." Wouldn't he be incredibly disoriented, maybe even suspicious or resentful of Hamlet?
Admittedly, there's a lot less to go on with Horatio because we rarely see him doing anything but agree with Hamlet. You'd have a lot of liberty to decide what he does between Act I, Scene 5 and Act III, Scene 2. Where does he go? Does anyone notice his inner conflict? Does he at any point make up his mind not to help Hamlet, only to change it later? Whom does he spend time with? What are the conversations like? Remember that in Act IV, Scene 5 Claudius asks Horatio to go with Ophelia as she exits, which suggests the two might have some sort of friendship. Wouldn't that make for an interesting conversation—Horatio and (maybe crazy) Ophelia about the behavior of the man they both love?