A lot of types or genres of fantasy can be distinguished. The categorization of the genres is often not clear but vague and/ or overlapping. Also several names are used to describe the same or similar fantasy genres.
Below an overview of the main types of fantasy as I would categorize them. It is by no means a complete list of fantasy genres but I think that most people would agree that it contains the main genres and could be used to classify almost all fantasy books and series. As indicated before, the exact definition and categorization of the genres is often unclear and different views on it exist. Therefore, my interpretation of the different genres may be up for debate.
High Fantasy / Epic Fantasy
High Fantasy and Epic Fantasy are sometimes discussed as separate types but I consider them to be the same.
This type of fantasy is characterized by stories that are happening on an epic scale in a world completely different from our own. Strange beings, great battles and lots of magic.
Most of the popular fantasy series and books are part of this category with the best know example of course being The Lord of the Rings.
This category of fantasy almost always revolves around the typical story of a young boy who turn out to be a great hero.
It can be seen as a subgenre of high fantasy. Many if not most high fantasy stories have such elements but some books/ series completely revolve around it.
Closely related is Sword & Sorcery genre, which I consider to be a more extreme version of Heroic Fantasy. A good example of Sword & Sorcery is Robert E. Howard’s Conan the Barbarian.
Low Fantasy is probably the most vague category of fantasy. To me, Low Fantasy stories are set in a relatively normal world, containing some fantasy elements. Magic is most of the time on the background (dormant) and when it does play a role it is more subtle compared to high fantasy.
A Song of Ice & Fire I would consider to be High Fantasy, but the series also has elements of Low Fantasy as fantasy is not the main focus of the series and magic only pops up every now and then.
Fantasy set in a historical setting, not in a thought-up fantasy world. Of course the story may not follow actual historical events but it uses a period from our past, often the Dark Ages, as the setting for a book. Fantasy elements, like dragons and wizards, are then added.
The story of King Arthur is an example of this genre.
Fantasy with a comedy twist. Books in this category not only contain humoristic stories set in fantasy realms but they are often also a parody or satire of “real fantasy” books, series or movies.
Several authors have picked fantasy as the setting for their humorous books with Terry Pratchett and his Discworld novels as the best-known example.
Fantasy in which scary creatures like werewolves and vampires are the main or important characters. This type of fantasy is closely related to the horror genre which is why it is sometimes difficult to draw a line as to what is fantasy and what is not.
Examples of dark fantasy is The Dark Tower series by Stephen King, the movie Pan’s Labyrinth or the computer game Diablo.
Fantasy in a modern-day setting, with the story at least partly happening in our real, contemporary world.
Clearly, the best-known example of this genre is the Harry Potter series but several popular movies and TV series are made in this genre, like the Twilight movies and the True Blood television series. The vampire theme is a modern setting is especially popular these days.
Stories that contain a mix of fantasy and science fiction elements. Often the evil side has powerful weapons while the characters on the good side are in touch with the earth or their inner selves and can use some form of magic.
One could argue that Shannara is related to this genre as the background story of this series clearly involve science. It is also a popular them for computer games, like Warhammer.
I hope this overview has created some clarity in the field of fantasy. Let me know if you have any additions or don’t agree with the distinctions made.