Well, since every story has been told in one form or another, I am a firm believer in character, character, character. I will read transfixed about a man or woman sitting on a park bench ruminating if the person is compelling enough.
Tension, creating enough interest to motivate the reader to move on.
It depends upon the genre, of course. And.....one must have some kind of satisfying conclusion to the story. Hate Alfred Hitchcock endings.
The basic ingredients of a story is depending on the type of story... what you want your readers to learn from your story. Every book has a reason it was written.
Intro, exposition, development, recapitulation, ending. Characters, situations, surprises.
Keeping the reader guessing and wanting turn the page. Providing accurate and informative information from page one to the very end.
A central theme of course. Characters and events that propel the story forward, and a solid flow from beginning to end, where the introduction and body of the work is resolved by the ending.
interesting plot and characters.
Realism. Even if you're writing fiction or science fiction there has to be a sense of realism. A thorough thought process that says this could happen, and a string that leads the readers through every chapter or scene. This keeps your audience interested, and makes them think.
I do fiction pieces for standardized testing and always try to create an interesting character. I remember when I took those tests (long, long ago) and how boring the passages were. I try to give my characters a purpose, a personality, and a sense of humor.
Forget the old rules is my first advice to an aspiring writer. The basics, of course, are place, time, characters and outcome, but there is a lot to fill in between page one and page... I find introducing new characters unexpectedly keeps the reader interested.
The usual: conflict, interesting characters, and a plot that moves. Things have to happen to hold reader interest.
A good plot line, strong characters, and the ability to show not tell (which takes a lot of practice).
fact, fun, story-telling skill, grammar and spelling integrity.
First there needs to be something that interests the reader in hearing the rest of the story. Then there needs to be a character worth knowing or an intersting concept and something interesting going on. The normal answers don't really suit me. I have written and also read stories that don't follow the normal patterns. Writing rules and art rules in my opinion are how the critics, who are not creators, try and confine and describe what those of us who create do.
Having said all of that I think that my childrens books are the hardest of all my creations because in a few lines I develop a character, get the reader intersted and tell a complete story. That is a lot to ask of so few words.
Beginning, middle, end. Good characters, a story that touches the soul, being able to evoke a feeling, making the reader care about the people in the story, that if you sat at a cafe table with them you would want to hear their tale.