Conflict, upheaval, crisis, or mystery...and then resolution. That's at the core of it. But you must also sketch memorable characters, settings, and circumstances along the way. Time and place are crucial to a great story. Can the author transport you there? Can the reader get lost in another world?
In my opinion, every story needs an excellent hook line to draw the reader in. And too, personally, I like to end with something to make the reader think. A few words they can take with them and reflect upon. Kind of like, giving them a reason for having read all 200 plus pages.
Characters. Obviously, you need conflic, crisis, resolution, but you have to care about the characters first. Good characters can save a dull plot; a good plot can't save dull characters.
Personal struggles, working with unknown factors, growth, evolution, the hero, or sometimes not... It depends on the story.
A story has a beginning, middle and an end. Each phase must satisfy internal criteria. The beginning introduces the tensions and levers by which the tension will be resolved. If it is too obvious the story will be boring. If the tensions aren't introduced, or the levers, then by the end of the story, the reader will be dissatisfied.
The middle part of a story shows the actions and interactions of the protagonist in their world. Antagonists have equal, or greater, footing. There may be developments, but nothing should be introduced that wasn't part of the start.
The end must satisfy the tension of the beginning. The reader should feel that all the levers came into play the way they should.
A story needs to explain the world, to show an aspect of life that might not be appreciated widely. This allows the reader to experience a feeling of achievement. It is also why Autobiography is such a well respected market, even though many of the writers aren't particularly good at it.
For me, the most crucial ingredient in any story is the characterization. If a story contains unbelievable characters for any reason, I find it very difficult to continue reading, and I pride myself on writing excellent characters in my own works. People and their interactions with one another fascinate me, and they fascinate me most when they grow to a level of complexity that requires deeper thought than they might appear to on the surface. In a fantasy world more than any other, you ought to be interested in the way that people live their lives, since they can often be so different (and yet, not so different) from reality.
Secondary to characters would be a strong plot. The plot doesn't have to be strong like a punch in the face, but strong like a well-made piece of wicker furniture, where every piece has its place, and weaves together with the others to form a unified whole in which nothing is overlooked or forgotten, no matter how small. Everything that happens to the characters should have some purpose, even if that purpose is not apparent at first.
Complex worlds and magic systems are my third requirement. I like worlds that are complex enough to make me think about how they work, but I don't go for things that are so complex that they require me to conduct a thesis on their inner workings. There is such a thing as being too detailed.
The three basic ingredients of any story are plot, characters, and the journey. Of the three, I see 'the journey' as the most important--where are you taking your reader and why? Of course to complete this trip you have to have a strong plot based on rich characters.
Baking Soda and/or Powder (depending on the genre).
A good story reaffirms your faith in life.
It seems self-evident, but story is the most important ingredient. A writer can create all sorts of dynamic characters with various degrees of tension and beautiful settings, but something has to happen. There has to be a story to tell, and a reason behind it.
Theme -- which one generally finds on the third revision
Characters -- who have strong emotions and/or strong viewpoints
An organic plot that rises from the characters' personalities and the events in the story.
A setting which brings out the theme and the characters' personalities.
Characterisation is for me, of the utmost importance. Then pace, for if a book meanders around the place, I tend to lose interest, with a fairly short attention span, unless it is fantastically written or hilariously funny. I think it's important to pepper narrative with dialogue, to 'show' rather than 'tell'. This keeps the reader engaged longer. Of course, a book needs some sort of plot, but it doesn't have to be action packed. I also think language is important. Too much repetition is offputting, and using less words has more impact than using too many.
Character. Time. Space.
Hard to say. Some stories, like those of Donald Barthelme, may not even have a "story." Others are almost entirely plot driven. Nobody's going to read The Problem of Cell 13, say, expecting great character development, angst, epiphanies, and hot sex scenes. Yet it's a great story. I tend to come at a story on its own terms, and try to take away what I perceive that the author wants me to take away from it. This has allowed me to enjoy a wide range of literature, and also to get angry at a wide range of literature, especially when I feel that what the author is saying he or she is giving me, and what I am actually being given are two different things. I don't like liars, bullshitters, or pompous gits.
Something that the reader can relate to....