Plot is not an essential ingredient in literature, but it is crucial to storytelling.
Envision plot this way:
You are a god. You have a planet (your setting) and on that planet you place a person (your protagonist) and then you merrily throw a problem at that person (your conflict) and then sit back and see exactly how that person deals with the problem (story arc). The person may fail or succeed, but in some way the person is a changed person by the end (resolution).
But what about the plotless story? Although the terminology of literature is anything but concrete, probably the most common definition of the plotless story, or vignette, is this:
"A vignette is a snapshot in words. It's different from flash fiction because you're not aiming to tell a story. The vignette focuses on one aspect, mood, character, setting or object. Use it as a descriptive exercise, for character exploration, wordplay or just to get something off your mind." -from eHow.com
"[a] sketch or essay or brief narrative characterized by great precision and delicate accuracy of composition. The term is borrowed from that used for unbordered but delicate decorative designs for a book, and it implies writing with comparable grace and economy." --A Handbook to Literature. 3rd. ed. C. Hugh Holman
This form of writing is a valid form, and is one of the more popular forms within the 'literary' genre, which is a style concerned with the manipulation of the language above all other concerns. Anyone who loves the qualities of language, the blend of sounds and meanings, will enjoy well-written vignette pieces. They may be fiction or non. They may be long or short, though I've never actually read a whole novel that ended without some kind of resolution. Vignette can perhaps be most accurately described as poetic prose.
Vignette is useful as a writing tool, to practice characterization, or setting, or narrative voice, or style. A journal entry is often a vignette--"This is what I did today..."--without any particular care for solving a problem or even completely finishing a thought.
Vignette may be a popular literary form, but if we're talking about popular fiction, the plot is king.
I found Bedford/St Martin's Interactive Fiction Tutorial useful in defining plot: "Plot refers to the series of events that give a story its meaning and effect. In most stories, these events arise out of conflict experienced by the main character."
So, plot isn't the story itself. It's the fire that fuels the progress of the story. The story is the action. Plot is what spurs the action. This event occurs (plot) and as a result, this happens (story). Imagine it as a string of beads. The beads are the plot points and the string between the beads is the story connecting those points. They work together to make a single cohesive string. The string without the shiny interesting beads would be dull. The beads without the strong string would never hold together. Like a string of beads, a plotted story has a beginning, in which conflict spurs the protagonist to act, a middle in which he seeks answers and a solution, and an end in which he finds some kind of solution.
Many writers outline stories following a plot diagram or list. This happens, then this happens, then that happens. But it's when a writer fills in the details between the events that a story is born, that characters come to life, that the events are put into context and are made meaningful to the reader.
Walk into any Barnes and Noble and you'll see shelf after shelf of popular fiction. Mysteries, historical fiction, science fiction, fantasy, westerns, romance, mainstream fiction. They all have something in common. They all have plots. You'll find those plots boiled down in a few paragraphs on the jacket/cover blurb. They all have some god behind them (whose name usually appears on the front cover) who throws problems at their people to see what happens. And at some point before the end of the book, usually very close to the end of the book, the people solve their problems in some way.
I've heard it said, and believe it to be true, that a well-constructed plot should be simple enough to summarize in less than 25 words. In fact, I've heard it said that summarizing your plot in less than 25 words (and by that I mean complete sentences) is an excellent way of boiling plot down to its core, and that those 25 words are what an agent will allow you to sell your story in a query letter. I've tried it. It's a valuable exercise.
Try it. Identify the protagonist's problem, how the problem causes the protagonist to react, and how the protagonist solves the problem. If you're unable to identify these three elements, your story may not have a plot. That's fine. Just realize that most fiction that sells well has plot.
So, why do we love plotted stories?
I'm not going to psychoanalyze. I'm just going to tell you what I feel in my gut.
Life is, and always has been, a series of uncertainties. In this day, some of us don't even know where the next paycheck is going to come from. We don't know what tomorrow will be like, we don't know where we'll be in 10 years, we don't know how our life will end, we don't know what's beyond this life.
Plotted stories give certainty.
Plotted stories end.
Plotted stories show someone--hopefully someone we can relate to on some level--facing and resolving a problem.
In plotted stories we see characters deal with problems and win.
But sometimes our characters don't win. That's a valid solution. Because sometimes WE don't win. But when the character doesn't win, he changes in some meaningful way. He grows, he gains enlightenment. If more of us lived our lives seeking meaning and growth and enlightenment from our experiences, our world would be a better place filled with better people. But that's just my opinion.
From stories we learn how to live. We learn how to lose, we learn how to love, how to gain knowledge. Through stories we share this knowledge, we teach.
Stories are memorable, meaningful, far more than merely entertaining. Or they should be.
While these values can be conveyed to some extent through non-plotted stories, a plotted story gives us something additional that all humans crave. We hear it discussed on Dr. Laura and Dr. Phil, it comes to the surface when we face grief or stress.
Closure. Resolution. We want things resolved, finished, wrapped up neatly. Otherwise we feel unfinished or left behind.
A well-written vignette can capitalize on those emotions, using them to create dischord through incompleteness. That's fine, if you like that sort of thing.
But most of us like things finished. That's why we love plotted stories.
So, should you plot or not?
I don't care.
It's another decision for you, the writer, to make, knowing that every decision you make will have an impact on your readers, for good or bad. It's impossible to make every reader happy. Don't try. Write to make yourself happy. Somewhere out there is someone who will love your story--plotted or not--and hopefully, someone who will buy it.
But if you want any hope of making Dan Brown or Stephen King kind of money, you'd better learn to plot.
For a short article on plotting:
Top Ten Plotting Problems by Alicia Rasley
For one of my favorite plotted stories:
"Into the Cellar" by Ajani Burrell
A beautiful but completely plotless, language-centered Vignette:
"Meaning of Life #31" by Sean Lovelace
And a Vignette with some elements of plot but little or no actual resolution and not much overt story, but still very well-written:
"Home Economics" by Gail Louise Siegel