In Act III when Leontes learns not only that his wife Hermione was innocent of adultery but that his insane jealousy has cost her life and that of their young son. Also, Paulina's bold, toe-curling lambastement of the grieving Leontes. This troper has seen a number of Shakespeare's plays at Ontario's renowned Stratford Festival, but not until that play and that moment did he hear that many simultaneous sniffles from an audience.
And the scene at the end when the 'statue' of Hermione comes to life — happy tears, in that case, but still!
The ending is pretty sad in its own way. Yes, Hermione has come back to life and Perdita has been returned to her real parents, but Leontes and Hermione are both aged, nothing can bring Mamillius back and Leontes will always have to live with the mistakes he's made and the years he and his family have lost because of them.