Antony And Cleopatra. Who have even less excuse for this than Romeo and Juliet, seeing that they're not teenagers and that they are two of the most powerful people in the world. Antony ignores the advice of his generals to fight on land, and fights at sea because Cleopatra wants him to. Halfway through the battle, Cleopatra gets frightened and orders her ships to flee, and Antony orders his ships to FOLLOW HER. Naturally, he loses the battle, and blames Cleopatra. To test whether Antony still loves her, Cleopatra sends him a messenger bearing word that she is dead. When he hears this, Antony decides to kill himself, but he's almost too much of a coward to go through with it, and stabs himself in the wrong place so that he is badly wounded, but not yet dead. THEN Cleopatra sends another messenger to say "Oops, I was just messing with you!" What makes it worse is that this actually happened in Real Life. Antony and Cleopatra really were that dumb!
So Hamlet just found out that his dad was killed by his uncle, but he still wants to spy around and make sure that the ghost was telling the truth. Fair enough. And then he decides to pretend to be insane, for absolutely no reason at all. There is no suspicion on him at this point and the uncle has no idea that the ghost even exists, let alone that it might warn Hamlet of what happened. Of course, his insane act is what gets everyone suspicious in the first place and sets up for the massive death scene at the end.
Depending on the performance, Polonius could also count. Towards the end of the play, he decides to hide in the queen's bed chambers to spy on her conversation with Hamlet. As things go on, he panics and starts screaming for help, leading a very paranoid Hamlet to run him through. If the actor playing Hamlet is sufficiently insane and frightening, it's a bit more understandable. Otherwise...
In Pokemon The Mewsical, most of Team Rocket counts. Several Rocket Grunts annoy Giovanni and are shot as a result, and one Grunt reports that an agent fought a boulder for twenty minutes because they mistook it for a Graveler.