{novel} The novel is a story with more than one chapter.
{fluff} A fluff story is one that is light and "fluffy", which is where it gets its name. These are almost always romantic.
{lemon} A lemon is a story that is almost always rated NC-17 and involve the characters engaging in vividly described sex. The whole point of it is sex. It's for the pervs.
{one-shot} The one-shot is a story that is only one chapter but can't be classified as fluff or a lemon.
{crossover} A crossover is a story that features more than one band. Janne da Arc meets Kagrra. MUCC meets Kiyoharu. Kyo meets Takanori. You get the idea.
{interactive} Second to lemon, this is the best kind. In this story you get to decide what happens to the character. You'll read a scene and then have options at the bottom of the page for where you want to go next. These always have a plethera of scenarios and usually have multiple endings.
{AU} AU or "Alternate Universe" stories are some of the best. These are just as they say: alternate universe. Sugizo's a vampire in the 16th century. Miyavi's a pirate in 1843. Kaoru's the captain of the S.S. Spacey exploring the unknown galaxy in 2062. You get the idea. ^_~
{parody} A parody can be anything from different lyrics to a renowned song (i.e. - "I Want Visual Kei" instead of "I Want It That Way") or a story that makes fun of another story that's well known (i.e. - "Camui Gackt and the Half-Man Princess" instead of "Harry Potter and the Half-Blood Prince"). These are always funny and usually stupid, but worth it.