"Formula" is an ambiguous term, and I should define how I mean it. I will give a basic example, found across genres such as jokes and Three Act plays. It has three steps.
Step One: Protagonist does something wrong.
Step Two: Protagonist does something wrong again.
Step Three: Protagonist finally gets it right.
General enough? TOO general to be useful? This definition of formula can be just another word for story structure. All stories have it, with the possible exception of some experimental works that go out of their way not to, in the same way some modern art goes out of the way to eschew beauty. This is not to say that there is no difference between formulaic fiction and quality fiction, however. In formulaic fiction, the formula is all there is to the story, whereas beautiful literature transcends the form. In one case, the formula is all there is in the end, in the other, it is merely the starting point, a vessel to hold something else.
Maybe a stricter use of formula would be helpful. Here's another example of some formulas, formula as trope, as predictable plot:
The Protagonist is given a chance to re-live some period of his life as if he'd made a major life decision differently.
Step One: Protagonist is wrenched from present life into alternate reality life
Step Two: Protagonist tries repeatedly to re-establish old life
Step Three: Protagonist finally learns to value alternative life.
I trust we all know and abhor the danger of predictable plots and trite tropes. We also know that certain genres require a certain degree of formula, the HEA in Romances, the dead body and list of suspects for Mystery, etc. Though I am curious to see what Scott F. Bailey does to the detective story.
What interests me, however, and the reason I began with such a general definition of a formula, is why we gravitate toward formulas at all. Because I think this scratches at the surface of an even deeper question, which is why do we even write fiction? We human beings are great liars, but it still boggles the rational alien as why we would not just lie to someone we want to sell used cars to but that we would pay money to read long elaborate lies. Why don't we read only true stories, lists of facts, figures? Why, when we read fiction, does that fiction almost always follow regular rules of production, formulae? And if we try to eschew formula fiction, what are we left with? Are there still rules of good writing, narrative structure and plot arcs that we need to follow?