In Dog Sees God, the character Matt is a homophobic bully throughout, his main target being the gay musician Beethoven, but he fully crosses this when he breaks Beethoven's hands so badly that he can never play the piano again. This is what causes Beethoven to commit suicide.
In Giselle, it appears that the curse of the wilis only stays in effect if they had already danced a man to death; considering that Giselle's refusal to let Albrecht die on her first night with the wilis causes their spell over her to be broken and allows her to pass on, it's pretty clear that the other wilis have already crossed it before the start of the story. God only knows how many men they had murdered before they intercepted Hilarion...
Claudius crosses by murdering his brother before the beginning of Hamlet.
In Henry V we are expected to root for the English over the French, despite the fact that the English have a very flimsy justification for going to war and the play admits this. So to make sure the audience knows the French are nasty customers, Shakespeare has the French soldiers, when they realize they're going to lose, massacre the teenage boys who carry the english army's supplies, one of the highest war crimes possible in those days.
Hera crosses it in Herakles Mad when she fills the title character, who has just defeated a tyrant, with a homicidal rage simply because he's one of Zeus' bar sinisters.
The blinding of Gloucester marks Cornwall's crossing in King Lear. Goneril and Regan possibly also cross at this point if they haven't already with their treatment of their father.
Regina in The Little Foxes is greedy and morally bankrupt as it is, but she crosses the event horizon when she lets her husband Horace die of a heart attack because he won't go along with her scheme.
The titular character in Macbeth (the play for which the page image is an illustration) reaches this point when he has Macduff's family, including the kids, murdered.
Medea. She convinces two kids to cut up their father and put the pieces in boiling water, making them think it'll make him younger. And that's even before the scene when she puts the children she had by Jason to the sword.
She crossed it even before they got back to Argos when she chopped up her younger brother and tossed the pieces into the ocean so that her father would have to delay his pursuit to gather the pieces for a proper burial. This was so awful that Jason's intervention was the only thing keeping the rest of the Argonauts from tossing her overboard too.
Though, most of these (aside from murdering her brother) weren't included in the story until Euripides introduced the idea that she murdered her children. Up until that point, she was more of a deeply flawed Woobie, Destroyer of Worlds, since Jason was kind of a bastard to her.
Iago's crossing in Othello is the enactment of his plan to ruin Othello.
The eponymous man in The Phantom of the Opera crosses the MEH when he ties Raoul to a noose and forces a Sadistic Choice on Christine; either confessing love for the Phantom and buying Raoul's freedom, or confessing love for Raoul and watching him die.Lampshaded in Christine's song lyrics: "The tears I might have shed for your dark fate, grow cold and turn to tears of hate!" Though she still pities him by the end anyway, so maybe this doesn't qualify.
Note the lyrics in his half of that Dark RepriseCounterpoint Duet: "Past the point of no return, the final threshold—the bridge is crossed, now stand and watch it burn!"
Similarly, Richard III probably hit it when he had the princes murdered. Even the play itself indicates that he's crossed a line: up until now, Richard has been cajoling his audience and sharing his plans and ambitions. Immediately after the princes' deaths, though, Richard suddenly loses all of his charm and verve, like a rapidly deflating balloon.
Seneca's play Thyestes is about King Atreus' Moral Event Horizon. Mad at his brother, the title character, for stealing his wife and attempting to steal the throne, he pretends to call Thyestes and sons back from exile and serves Thyestes his own sons for dinner and takes great pleasure in telling him "you ate your children".
Stanley's crossing of this in A Streetcar Named Desire came when he raped Blanche to insanity and then lied that he never once touched her afterwards.
In Titus Andronicus, Tamora, Demetrius, Chiron and Aaron all cross the MEH with Lavinia's rape and mutilation.
Caldwell B. Cladwell crosses this when he orders Bobby Strong to be sent to Urinetown, which is actually being thrown off Cladwell Column, knowing full well that his daughter will probably be killed by the rebels. Necessarily Evil or not, that was just unpardonable
In Wicked, at least as far as Elphaba was concerned, the Wizard crossed the horizon when he broke Professor Dillamond's will, turning him from a respected professor into a mindless animal. For Mrs. Morrible, the horizon mark came when she created the cyclone that brought Dorothy to Oz(and killed Elphaba's sister Nessarosa). Interestingly enough, once Glinda takes the reins of government, she is willing to simply exile the Wizard from Oz (this might be because he's realized — to his horror — that Elphaba, whom everyone believes is dead, was his daughter), but has Morrible sent to prison.
Greek tragedy has a term for this event: Harmatia. It's the act the Tragic Hero performs, usually motivated by his "hubris" (Tragic Flaw), that starts the tragedy down the path of no return. Normally this is some kind of offense against the gods or against the natural order: a murder, an act of blasphemy, a rashly-taken oath, etc. But once committed, it can't be undone. The Tragic Hero and every character around him is doomed, no matter how hard they try to escape their fate.
Peer Gynt plays with the trope. Although it seems Peer Gynt himself is about to cross the Moral Event Horizon a number of times, he secures himself by hovering juusst over the edge of it. He even lampshades this as his leading principle. It occurs to him, a little late in life, that this constant playing with the trope gains him a Fate Worse Than Death, and he crosses the Despair Event Horizon instead. And this freaks the living batshit out of him.