The ending of Othello when Iago's wife comes in and tells Othello what really just happened. Say what you want about the play; that breaks the heart.
That scene is heartrending for just about everyone involved. Watching Emilia gradually realise that a) her friend is dead, b) Othello killed her, c) her own husband persuaded him to do so, and d) oh, and it's sort of her own fault too.
Desdemona's very death itself; as her husband's trying to kill her she screams things like "Kill me tomorrow, let me live tonight!" and plead to be allowed to say one prayer.
Desdemona's final words, when they're left in. When given the opportunity to name her killer, she says it was herself. When put in context, it's a very Christian woman telling a lie on her deathbed, condemning her to hell because she still loves Othello too much to cause trouble for him.
In the times when they aren't left in the last thing she does before dying is caress Othello's face. It was both letting him know she still loved him even after all he did to her, as well as silently asking "Why?".
In keeping with the above, in spite of the violence and death, the love between Othello and Desdemona is still heart-rendingly obvious in the chamber scene. His monologue watching her sleep has many lines commenting on how beautiful and sweet she seems, and being wracked with anguish about hurting her in any way: "Yet I'll not shed her blood/Nor scar that whiter skin of hers than snow/And smooth as monumental alabaster/Yet she must die, else she betray more men." When she wakes, the first thing he asks her is if she has said her prayers, and confessed her sins, because he doesn't want her soul to be unabsolved before she dies. Even mid-way through strangling her to death, he presses the pillow over her face, saying, "I will not let thee linger in thy pain." All those subtle signs of affection, combined with Desdemona's final words, will turn you into a blubbering mess if the production is doing its job.