@Literaticat has posted a list of genre definitions. Perhaps the most useful paragraph for beginners is this one (emphasis/shouting hers):

PLEASE NOTE: YA, MIDDLE GRADE, PICTURE BOOK, GRAPHIC NOVEL, FICTION, NON-FICTION & BIOGRAPHY ARE NOT GENRES. THEY ARE CATEGORIES. “Genre” is a further classification beyond category. If I were to use a Biology class analogy (bear with me, I had to go to summer school for Biology) I’d say that in the taxonomic hierarchy Kingdom-Phylum-Class-Species, “Kingdom” is book, “Phylum” is format of book (electronic, hardbound, paperback), “Class” is category (YA, fiction, etc), “Order” is big-genre, “Species” is sub-genre.

Then she wades right in with some examples:

URBAN FANTASY is always set in a city, and features um… FANTASY scenarios. For example, faeries that are addicted to drugs and live in the subway system. Or trolls who hang out in clubs and impregnate human chicks. Or whatever. If you haven’t written a dark and gritty fantasy set what we would recognize as a human-style city, you haven’t written an urban fantasy.

I agree with many of them, though not all. For example, I prefer the Historical Novel Society‘s definition of historical fiction:

To be deemed historical (in our sense), a novel must have been written at least fifty years after the events described, or have been written by someone who was not alive at the time of those events (who therefore approaches them only by research).

There’s also a lot left out. Where’s lesbian fiction? Where’s the Western? Novel of manners? The campus novel? And, oho-ho, The Great American Novel?

I think we could have some fun with this. We need both serious definitions (what exactly is ‘lesbian fiction’?) and more playful varieties. Here’s a Devil’s Dictionary-inspired description to get you started: Noir, the horror fiction of the crime genre.

What genres (and subgenres, and sub-subgenres) would you like to see defined?

Edited to add: a flowchart of genre (via Eric)