I bet you the current issue of Cosmopolitan has an article whose title begins with a number. "7 Things He Won't Tell You about Sex," or something like that. Some popular magazines feature articles of this type on the cover of every issue. That can't be happening by accident. Editors must know they attract readers.
Why do readers like the list of n things so much? Mainly because it's easier to read than a regular article.  Structurally, the list of n things is a degenerate case of essay. An essay can go anywhere the writer wants. In a list of n things the writer agrees to constrain himself to a collection of points of roughly equal importance, and he tells the reader explicitly what they are.
Some of the work of reading an article is understanding its structure—figuring out what in high school we'd have called its "outline." Not explicitly, of course, but someone who really understands an article probably has something in his brain afterward that corresponds to such an outline. In a list of n things, this work is done for you. Its structure is an exoskeleton.
As well as being explicit, the structure is guaranteed to be of the simplest possible type: a few main points with few to no subordinate ones, and no particular connection between them.
Because the main points are unconnected, the list of n things is random access. There's no thread of reasoning you have to follow. You could read the list in any order. And because the points are independent of one another, they work like watertight compartments in an unsinkable ship. If you get bored with, or can't understand, or don't agree with one point, you don't have to give up on the article. You can just abandon that one and skip to the next. A list of n things is parallel and therefore fault tolerant.
There are times when this format is what a writer wants. One, obviously, is when what you have to say actually is a list of n things. I once wrote an essay about the mistakes that kill startups, and a few people made fun of me for writing something whose title began with a number. But in that case I really was trying to make a complete catalog of a number of independent things. In fact, one of the questions I was trying to answer was how many there were.
There are other less legitimate reasons for using this format. For example, I use it when I get close to a deadline. If I have to give a talk and I haven't started it a few days beforehand, I'll sometimes play it safe and make the talk a list of n things.
The list of n things is easier for writers as well as readers. When you're writing a real essay, there's always a chance you'll hit a dead end. A real essay is a train of thought, and some trains of thought just peter out. That's an alarming possibility when you have to give a talk in a few days. What if you run out of ideas? The compartmentalized structure of the list of n things protects the writer from his own stupidity in much the same way it protects the reader. If you run out of ideas on one point, no problem: it won't kill the essay. You can take out the whole point if you need to, and the essay will still survive.
Writing a list of n things is so relaxing. You think of n/2 of them in the first 5 minutes. So bang, there's the structure, and you just have to fill it in. As you think of more points, you just add them to the end. Maybe you take out or rearrange or combine a few, but at every stage you have a valid (though initially low-res) list of n things. It's like the sort of programming where you write a version 1 very quickly and then gradually modify it, but at every point have working code—or the style of painting where you begin with a complete but very blurry sketch done in an hour, then spend a week cranking up the resolution.
Because the list of n things is easier for writers too, it's not always a damning sign when readers prefer it. It's not necessarily evidence readers are lazy; it could also mean they don't have much confidence in the writer. The list of n things is in that respect the cheeseburger of essay forms. If you're eating at a restaurant you suspect is bad, your best bet is to order the cheeseburger. Even a bad cook can make a decent cheeseburger. And there are pretty strict conventions about what a cheeseburger should look like. You can assume the cook isn't going to try something weird and artistic. The list of n things similarly limits the damage that can be done by a bad writer. You know it's going to be about whatever the title says, and the format prevents the writer from indulging in any flights of fancy.
Because the list of n things is the easiest essay form, it should be a good one for beginning writers. And in fact it is what most beginning writers are taught. The classic 5 paragraph essay is really a list of n things for n = 3. But the students writing them don't realize they're using the same structure as the articles they read in Cosmopolitan. They're not allowed to include the numbers, and they're expected to spackle over the gaps with gratuitous transitions ("Furthermore...") and cap the thing at either end with introductory and concluding paragraphs so it will look superficially like a real essay. 
It seems a fine plan to start students off with the list of n things. It's the easiest form. But if we're going to do that, why not do it openly? Let them write lists of n things like the pros, with numbers and no transitions or "conclusion."
There is one case where the list of n things is a dishonest format: when you use it to attract attention by falsely claiming the list is an exhaustive one. I.e. if you write an article that purports to be about the 7 secrets of success. That kind of title is the same sort of reflexive challenge as a whodunit. You have to at least look at the article to check whether they're the same 7 you'd list. Are you overlooking one of the secrets of success? Better check.
It's fine to put "The" before the number if you really believe you've made an exhaustive list. But evidence suggests most things with titles like this are linkbait.
The greatest weakness of the list of n things is that there's so little room for new thought. The main point of essay writing, when done right, is the new ideas you have while doing it. A real essay, as the name implies, is dynamic: you don't know what you're going to write when you start. It will be about whatever you discover in the course of writing it.
This can only happen in a very limited way in a list of n things. You make the title first, and that's what it's going to be about. You can't have more new ideas in the writing than will fit in the watertight compartments you set up initially. And your brain seems to know this: because you don't have room for new ideas, you don't have them.
Another advantage of admitting to beginning writers that the 5 paragraph essay is really a list of n things is that we can warn them about this. It only lets you experience the defining characteristic of essay writing on a small scale: in thoughts of a sentence or two. And it's particularly dangerous that the 5 paragraph essay buries the list of n things within something that looks like a more sophisticated type of essay. If you don't know you're using this form, you don't know you need to escape it.
 Articles of this type are also startlingly popular on Delicious, but I think that's because delicious/popular is driven by bookmarking, not because Delicious users are stupid. Delicious users are collectors, and a list of n things seems particularly collectible because it's a collection itself.
 Most "word problems" in school math textbooks are similarly misleading. They look superficially like the application of math to real problems, but they're not. So if anything they reinforce the impression that math is merely a complicated but pointless collection of stuff to be memorized.