I've been rethinking fantasy definitions some more. I continue being dissatisfied with existing fantasy definitions, so I've written some more of my own.
Quest Fantasy - A fantasy whose story revolves around a (usually) clearly announced endpoint. The protagonist(s) then go about doing what needs doing to reach that clear endpoint. The structure consists of learning the goal, encountering difficulties reaching the goal, accomplishing the goal, and then wrapping up the storyline.
Heroic Quest Fantasy - In this style of fantasy, the protagonist acts to set the world to rights, using his abilities not for himself, but for the sake of everyone else. The hero tends to be a prime motivator. Classic examples include Lord of the Rings, Beowulf, Star Wars (Episode 4).
Unheroic Quest Fantasy - In this style of fantasy, the protagonists acts to his own advantage, using his abilities to preserve himself and improve his own position. The hero tends to be an opportunist, often having unadmirable traits.
Military Quest Fantasy - In this style of fantasy, the protagonist does what he's paid to do. He is often called upon to do unsavory things. The protagonist tends to be a mercenary, often having little or no control over what happens. If the protagonist does have control, his control is finite. Notable examples include The Black Company.
Serial/Epic - Any of the above can be stretched out into long books (Epics), or broken apart into many books in a row (serialized). Each individual story is self contained, but the final goal is present through all the books. For example, in Harry Potty, the defeat of Valdimort is the final goal, even if all the stories between are about something else.