EUOL, I just spent an entire semester arguing with classmates over the different sub-categorizations within fantasy and what fantasy is. At least within children's literature, there's wide disagreement about what should be considered in the realm of fantasy and how the larger genre should be subdivided. Here's the subcategories I came up with for that final project I was working on. They're fluid, though--some are more for convenience of fitting them into some place, and could go in more than one category, or don't really have a category. (These are not in any particular order, and some might be considered subcategories of another if I thought about it enough.)
Myth, folklore & legend
Turning the old stories on their heads (or, sometimes, not)--Retellings of fairy and folk tales--Using the old stories--fairy, myth, and legend--to fuel new ones
-Fairy/folk stories after the British tradition (including all Celtic traditions, English, Scottish, Welsh, and Irish)
-Fairy/folk stories after non-Western traditions
Satire/tall tale/humorous
Toy stories
Witches, sorcerers, and dragons (and other magical people/creatures)
The Quest/High Fantasy
Portals to other worlds
Parallel worlds
Ghost stories
Animal fantasy
Non-human people and/or other weirdos
Wishes
Magical realism
Time Travel (sometimes fantasy, sometimes science fiction)