Fairy Tale, Fable/Parable, Satire, Folklore, Legend, and Mythology, Oh My!
If you thought all 156 of Andersen's tales would be in the same genre, well. You're wrong! Maybe for the first time ever? Heck, some of Andersen's tales don't even belong to recognizable genres, unless you count "Short Sentimental Philosophical Musings on the Nature of Art" as a genre. Below we'll go into some of the more frequent, mainstream genres you'll encounter while reading Andersen's tales.
Fairy Tale
Duh. That one's a no-brainer, since Andersen's best known for his fairy tales like "The Little Mermaid," "The Princess and the Pea," "The Snow Queen," and so on. Some of his lesser-known stories also fit the bill, what with their emphasis on magical transformations, quests, and happy endings and all—"The Traveling Companion," "The Wild Swans," and "Inchelina" (better known as Thumbelina). Not all of Andersen's fairy tales have happy endings, though (remember his version of "The Little Mermaid"?) and some of them, like "The Wild Swans," have more of an emphasis on God and religion than you'd see in other fairy tales. So keep these differences in mind as you read on, and don't come crying to us if the lovers you thought were going to get married end up separated, dead, or both. Can't say we didn't warn you.
Fable/Parable
We're lumping these two together because they both have moral messages. The only difference is that fables usually have animal characters and parables usually have people characters. And Andersen's characters can be either or both. Like in "The Naughty Boy," Cupid (a.k.a. the god of love) is personified as a little boy who naughtily goes around shooting people with his arrows and making them fall in love. The message is that we're all gonna get hurt by love at some point in our lives, regardless of whether the deliverer of that message is deity, human, animal, vegetable, or mineral. In other tales, like "The Buckwheat," we see the plant representing an inability to bend and adapt to new conditions. So, again, there's a message in the story, and it's not just that whole grains are delicious and nutritious.
Satire
Andersen sometimes used his stories to criticize aspects of humanity that he didn't like. In "The Emperor's New Clothes," we see vanity and gullibility being ridiculed. In "'Something'," the main character becomes a critic and makes his living pointing out other people's flaws and mistakes. Fun times.
Folklore, Legend, and Mythology
The fairy tales that Andersen wrote obviously utilize folklore. But, to be more specific, some of his stories are based on legends: tales that are told as though they could be true. Others are based on folktales: fictional tales circulating within peasant communities. "Little Claus and Big Claus" is a great example of a folktale in which our witty, downtrodden protagonist outwits the rich dude and makes off with his wealth. No fairy godmothers or anything to help him out, just plain ol' inventiveness and folk wisdom.