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To me, the most powerful fantasy embodies archetypes, like folklore and mythology do and classic literature often does. It is easiest to deal with archetypes, dream images, and many other fundamentals of human psychology in fantasy, which echoes the earliest stories of our childhood and the human race's childhood.
If you do want to analyze it some more, I found an excellent literary treatise FANTASY [through 1985] on the web.
Ultimately, I define fantasy by reference to stories that I consider fantasy.
The Forgotten Beasts of Eld, by Patricia McKillip, is one of the classics of fantasy. The review I've linked to calls this "high fantasy", which seems to fit. "High fantasy" is fantasy dealing with wizards, elves, magical beasts -- what most people think of in reference to "fantasy".
The Little Country, by Charles de Lint, is another classic. This is an example of "urban fantasy", by one of the pillars of the genre. "High fantasy" tends to take place "long ago and far away", usually in a low-technology setting. In urban fantasy, the setting is updated to our own modern world, yet the elements of magic and myth and archetype are kept. It takes a great deal of talent to make this work without making it a comic parody, but de Lint has the talent.
The Empire of the East, by Fred Saberhagen, is harder to classify. I located a review at http://sf.www.lysator.liu.se/sf_archive/sf-texts/REVIEWS.INDEX, by Eric S. Raymond, very short. As he says, "Is this post-holocaust technology-of-magic SF, or heroic fantasy with rivets for flavor?" You've got gods, heroes, magic, a coming-of-age quest, and a whopping big army tank -- you want to quibble about categories? As Eric says, "...it's powerful stuff, a grabber from page one. Enjoy!"
Mojo and the Cookie Jar by Douglas Bell is another example of urban fantasy -- and comic fantasy. It's an example of a lot of things, all mixed together. It won the Philip K. Dick Award in 1991. It's out of print, but look for it -- it's worth the effort.
I don't think you need a definition of comic fantasy, do you? If you
do, pick up any Discworld book by Terry
Pratchett. You'll get the definition.
Pratchett info and links: a fan page
Master of Comic Fantasy
a bibliography on Inkspot
Mistress of Fables
SCI-FInder, the dedicated science fiction & fantasy search engine
IF YOU LIKE THIS, THEN YOU'LL LIKE THAT page of the Ultimate Science Fiction Web Guide from MagicDragon Multimedia
SFFBooks sf and fantasy book discussion list and website.