"The Young King", especially the coronation scene where God himself approves of the humble new sovereign when his own noblemen reject him. "A king higher than any of us has crowned you, my son!"
The LibriVox recordings don't help either- one set, "The Happy Prince" and a couple of others, is read by a woman with a rather soft voice and a very cute accent. It makes it much, much worse. In "The Remarkable Rocket", she manages to make a damp firework (albeit an anthropomorphic comic relief firework) come across as incredibly moving and highly tragic.
"The Fisherman and His Soul": Its power as a Tear Jerker is even lampshaded in the end, when the priest who ordered that the bodies of the fisherman and his mermaid girlfriend be buried in unconsecrated ground tries to speak in his homily about the Ire Of God, but he can't do so and speaks about the Love Of God and makes his audience bawl. And then he finds out why... the flowers in the church come from the Star Crossed Lovers' tombs.
"The Birthday of the Infanta". A hunchbacked dwarf is sent to perform for the Infanta of Spain, who is only allowed to mingle with other children on her birthday. She and the other guests laugh at the dwarf's performance and request an encore after dinner, but the dwarf mistakes the Infanta's mockery for love and searches the palace for her. Eventually, he is horrified to discover a hideous figure who mimics his every move... and realises it is his own reflection, and that the Infanta can never return his feelings. He suffers a seizure and falls to the ground kicking and screaming; the Infanta and her fellow guests find him and mistake it for another performance, laughing at him once again until he stops moving or breathing. A servant tells the Infanta that the dwarf has died of a broken heart, and the chastened Infanta declares, "For the future, let those who come to play with me have no hearts."
"The Selfish Giant" features the title character building a giant wall around his garden to keep playing children out of it, only for an unending winter to descend on the garden. Eventually, he hears a linnet singing outside his window - the children have found a crack in the wall and have returned to the garden, bringing the spring thaw with them. But when the giant runs into the garden to welcome the children, they all flee in terror except for one boy struggling to climb a tree. The giant takes pity on the boy and lifts him higher into the tree. He then knocks down the wall and gives the children a standing invitation to play in his garden, but he is disappointed when the boy, whom none of the other children had seen before, does not return with them. Eventually, he finds the boy alone in the garden, bleeding from his hands and feet; he sees the wounds and threatens vengeance against those who inflicted them, but the boy explains that they are wounds of love, and reveals that he is returning the giant's kindness toward him by inviting him to his own garden, which is Paradise. The next day, the children find the giant dead under a tree, covered in white blossoms.
Basically every Oscar Wilde-penned bit of scribbling that isn't for the stage is worth a cry or two (and even then, watch out for Lady Windemere's Fan and A Woman Of No Importance), but especially De Profundis, Wilde's essays on Christ and Socialism, his letters to the newspapers about prison conditions, or anything he ever said about love, unless the reader wants to be wrung out like a dishcloth. And if the readers ignore the disclaimer above, they'd do well not to follow those pieces up with a perusal of Ellman's biography of Wilde, as it will likely leave them with the desire to dig up a few famous corpses and strangle them; the man is utterly Moe.
"The Ballad of Reading Gaol", written just after his release from the titular prison.
"Something was dead in each of us, and what was dead was Hope."
"I know not whether Laws be right, Or whether Laws be wrong; All that we know who lie in goal Is that the wall is strong; And that each day is like a year, A year whose days are long."
And the excerpt that was made epitaph on Wilde's tomb,
"And alien tears will fill for him, Pity's long-broken urn, For his mourners will be outcast men, And outcasts always mourn."
If you read up more on the Wilde family after Oscar's arrest, it turns into a Tear Jerker. Constance dies, leaving her sons in the care of her family who try to bar them from seeing their father ever again. The sons finding out about his death and what got him arrested. Cyril, Wilde's eldest son, is killed by a sniper serving in WWI. Wilde's youngest son, Vivian, loses his wife before he comes home from WWI... it's amazing that Vivian made it to 80 without losing his mind to grief.
Some of his letters to Bosie from the jail. Especially the third of these.