Dramatic Irony of the Prince
The Prince (in The Little Mermaid) is unaware of the Little Mermaid's mythical nature, perceiving her to be human after she drinks the potion. He is also ignorant to the fact that it was she that saved him from the storm, as he did not catch sight of her.
Tragic Irony of the Mermaid
Culturally, merpeople and sirens are known to be tragic heroes, with the original Greek mythological mermaid (Atargatis) accidentally killing her lover. Thus from the onset the educated reader understands that the Little Mermaid is doomed to failure in her quest for the prince's affection, even if she herself is unaware. There is also a sense of irony evoked through forcing the mermaid to give up its defining feature.
Irony of the Magic Mirror
From the opening of The Snow Queen, we learn about the effect of a magic mirror made by the devil that shattered into splinters and falls into the eyes and hearts of its victims, causing them to lose their innocence. The male character, Kai, falls victim to this mirror but the protagonist Gerda is unaware until later in the novel. This is important as while she is not aware of the cause of the change in Kai's behaviour, she remains unrelentingly loving towards him.
Irony of the author as protagonist
Critics have often pointed to the fact that the author protagonist of The Shadow, a fairytale about a protagonist (who is an author) losing his shadow. The poem is said to be about Andersen itself, operating as an expression of the relationship between author and his work. Because of its extreme irony, many consider it to be more of an "anti-fairytale" than a traditional fairytale in its own right.
Dramatic Irony of the Emperor
There is undeniable irony in The Emperor's New Clothes, whereby an emperor who is obsessive over his clothes ends up parading his nakedness to his subjects. This irony emphasises the incompetence of the Emperor, an essential feature of the story.