The big gun of insight gained in Shakespeare's Hamlet is, of course, Hamlet.
His father's death and mother's hasty remarriage lead him to melancholy and depression, and a sense that existence is not inherently meaningful. The revelation by the Ghost that King Hamlet was assassinated by Claudius leads him to rage, but also to the weighing of evidence against Claudius, and to the thought that evil can disguise itself in order to do us harm. The speech by the 1 Player leads him to despair, when he compares his inaction to the player's appearance of great emotion, but also leads him to a concrete plan whereby he can determine Claudius's guilt with certainty. The discovery of Yorick's skull leads him to long for the past, but also to once again contemplate existence. The death of Ophelia leads him to proclaim his love for her for the first time in the play.
Hamlet is a thinker, and suffering leads him to thinking. He particularly is led to the contemplation of existence. And what is his specific insight concerning existence? That existence isn't worth the trouble, except for the fact that we don't know what lies on the other side of death; that, great or small (figuratively speaking), we all end up rotting in the grave, eaten by worms.