First, if you haven't seen it, I've got a pretty decent visual representation of most of the major genres out there.
HIGH FANTASY- This would probably be considered by most people (especially non-fantasy fans) to be the epitome of fantasy. The whole world has been created from scratch by the author. It is not our world, even if it looks an awful lot like Medieval Europe. Geography, culture, language, races, religion, dress, weaponry are all fictitiously created or mashed together for the purposes of the story. It's hard to find excellent, well-known examples of High Fantasy that are not Epic Fantasy. I say Graceling fits here, since it's a completely invented world, but focuses more on a plot-driven story with just a handful of dynamic characters. Similarly, The Princess Bride (though it is satire) could fit here, too (yes, Gilder and Florin are fake countries).
EPIC FANTASY - The distinction of "epic" refers to the scope of the story. Epic Fantasy is always High Fantasy, meaning it is in a fictional world and all elements of that world have been defined by the author. Epic Fantasy centers around a massive storyline, "Fates of Nations" and epic quests. The most well-known examples are also the most well-known examples of fantasy, period. Lord of the Rings, Sword of Truth, Shannara, Xanth, Narnia, Game of Thrones, The Belgariad.
PORTAL FANTASY - A character from our world is magically transported to another world via a portal of some kind. In Narnia it was the wardrobe (or the rings or just Aslan, depending on which story you're reading). In The Wizard of Oz it was a tornado. Doors, spells, gates, fairy companions, etc. If your character is from a mundane setting and gets transported to a fantastical world where magic is possible, you have portal fantasy. Lots of agents say this is overdone right now.
URBAN FANTASY - A fantasy that is set in our real world, often in a big city, though not always. Think magical elves in Central Park, fairies in Los Angeles, vampires in London. Portal fantasy will sometimes fit here, especially if the characters portal back and forth a fair amount. This sub-genre is very closely related to both magical realism and paranormal, differing from the first in scope and the second in character focus. Cassandra Clare's The Mortal Instruments series (and related series) would fit here. The Parasol Protectorate (Soulless), also fits here, though that's a steampunk story, too.
MAGICAL REALISM - This one is more of a contemporary, realistic story, in which magic plays a part. The world is so very much like ours, except for this one tiny piece of it. Often times religious stories will be recast with magic standing in for the power of deity, giving us magical realism. The most popular example I can think of for this sub-genre is actually a movie, not a book. Sandra Bullock and Nicole Kidman's movie Practical Magic is completely realistic and has both feet in our world, telling a fairly mundane story. Except they're witches. Similarly, Matilda would be another good example. Some people argue Harry Potter belongs here, other call it a portal fantasy and stick it up with Epic Fantasy.
PARANORMAL - There is not a huge difference between Urban Fantasy and Paranormal, it's more in the tone and the focus on character relationships. Urban Fantasy is written around the conflict, Paranormal is written around the interpersonal relationships and is more often than not a romance. The focus is usually on supernatural creatures, more so than magic. Twilight, How to Flirt with a Naked Werewolf, and Paranormalcy are popular examples of this sub-genre.
MYTHOLOGY - We don't write a lot of straight-up mythology these days, it's more like a reinterpretation of ancient mythology. But, still, we're relying on a magical, unknowable power to explain immortality and the powers of a handful of individuals to control the world. Percy Jackson is probably the most notable example.
LIGHT FANTASY - Some fantasy is not "hard" enough to be considered epic or high fantasy, but is too "other" to be described as contemporary
FAIRY TALES - A Fairy Tale relies on folklore or a "moral of the story" in order to tell the tale. We don't write a whole lot of these as original works anymore, they are usually in the form of retellings or reduxes. (is that how you pluralize that word???) In any case, we are taking existing fairy tales and twisting them around. In case you need examples: Cinderella, Snow White, The Goose Girl.
FAIRY TALE RETELLINGS - Keeps the original story but tells it in a slightly new way. Shannon Hale wrote some very popular versions of fairy tales in her Books of Bayern series.
FAIRY TALE REDUX - Takes the original story and mashes it up in some way. These have been very popular with the young adult set lately. Cinder, Twisted Tales
SCIENCE FANTASY - This is where science-fiction and fantasy collide. The focus is less on the science of the story/setting, and more of a "wouldn't it be neat if this was possible" and focuses on the story. Star Trek talks a lot about the science behind the story, how they got here, how they made that, developing new science, etc. Star Wars is a story that could be told anywhere, but it happens to be told in outer space. This is also where science fiction and fantasy mashups generally get placed, like Orson Scott Card's Pathfinder series, or The Lost Swords series. The stories feel like fantasy, but have a sci-fi setup or a sci-fi subplot.
Obviously it's impossible to define every single fantasy novel ever and put them all into neat little boxes. You can see Narnia popped up in two of my definitions here, and The Amber Chronicles are an excellent example of an epic fantasy that uses elements of portal fantasy and crosses into urban fantasy and science fantasy. There are arguments to be made the Cinda Williams Chima's Seven Realms series is high fantasy but not epic (though I say it qualifies as epic - four books, I'd guess around a half million words, fates of nations. That's epic, IMO)
What did I miss? What did I get wrong? Do you write fantasy? Do you read fantasy? What is your favorite kind?