I'll start at the end: the top will fall.
Take a moment. How do you feel? You're probably not satisfied, whether you agree or not. There's no relief to it, no "aha!" moment, no catharsis. That's because the top doesn't matter. You are looking at the wrong thing.
To explain how this can be known, you have to consider three metaphors that Nolan makes explicit.
First, the labyrinth:
Oh, look, a maze. And Ariadne auditions for Cobb by drawing mazes, and builds model mazes; and of course her name is neck deep in the metaphor of the maze.
But then nowhere in the movie is there an actual or metaphorical maze. Arthur says they need a maze to better hide from the projections, but they don't actually do this, right? When Ariadne draws her mazes for Cobb, he rejects the square mazes and is satisfied/stumped only by the circular classical labyrinth.
And anyway, mythological Ariadne didn't construct the Minotaur's labyrinth-- Daedalus constructed it for her-- she merely showed Theseus how to get out of it. But she didn't need to: a classical labyrinth doesn't have multiple dead ends; it is a single winding path that leads either in or out.
But Theseus, like the audience, upon being shoved inside wouldn't have known the form of the labyrinth-- dead ends or single path? So to be able to find the Minotaur, he needed to know which way to go, and Daedalus told him: downwards is the only way forwards.
And so it becomes clear: it's not an actual maze, it's a labyrinth, which brings us to the second metaphor: the paradoxical staircase.
A single path, that ends up back on itself.
The staircase defies geometry because it is fixed in a single perspective. If you alter that perspective, then the illusion is revealed.
Hence, Arthur and Ariadne can walk around and around the stairs passing the woman who had dropped her papers; and Arthur could sneak up on his attacker by going down the stairwell. When the perspective changed, then Ariadne and Arthur had to stop walking; then the surprised attacker could be pushed off a ledge.
But each of those times required a choice by Arthur to "see" the staircase from another perspective. Seeing it from a different perspective changed the reality.
Cobb's not trapped in a maze, he's trapped in a paradoxical staircase, covering the same ground over and over. He doesn't need Ariadne to lead him out; he needs her to clue him into another perspective.
The third metaphor seems to be the wedding ring. When he's in a dream, he wears a ring; when he is in real life there is no ring. So easy? Then why did Cobb insist on using the top-- something that Mal had touched and hence defeats the purpose of a totem? Why not just look at his ring? Well, give it a try yourself:
Pay close attention to how difficult it is to see Cobb's left hand. Right hands abound; left hands are hidden in pockets, under tables, in shadows. Now that I've said it, you'll be astonished at how obviously deliberate it is that DiCaprio is hiding his left hand from us-- except at certain moments. Nolan is actively frustrating your attempts at determining whether it's a dream or not.
Why so many long gun battles and fight scenes? Can't they just dream of being at the safe or past the bad guys? No. That's how we signify (male) conflict in movies; on the way to catharsis, you have to fight.
All of this is the expression of the third metaphor, which is really the theme of the movie: resistance.
Does Inception remind you of The Matrix? The Matrix brothers wanted you to reference Baudrillard's idea of a simulated reality substituting for "real" reality. However, their execution was flawed.
The Matrix is a great movie but a poor expression of Baudrillard's philosophy. The Matrix is quite straightforward, there's no confusion, no paradox: you're either in the Matrix, or you're in the real world. You may not know you're in the Matrix, but that doesn't change the fact that you are, or are not, in it.
A true Baudrillard Matrix would be a single fake world that became so real that you no longer needed the original. The whole world becomes a fake; there is no recourse to the real world. You'll know it happened when you look at a copy of something, the original of which you have had no actual knowledge, and say, "oh, that's so authentic."
The dream does not have an external reference, it is not an illusion of reality, but a simulation not based on anything real. Cobb is specific about this when teaching dream architecture to Ariadne-don't use memories (which reference reality). What becomes real for Cobb and every other dreamer is the simulation. The dreamer merges their memory of reality with the architect's imagination into the symbolic. Only death is beyond the scope of the simulation-- and even that, levels deep, was a real possibility. Other than that the simulation becomes the reality. Fischer never reconciled with his dad, but Eames set him up to dream that he did, and upon waking behaves as if he did. He was shown a simulation of a reconciliation and merged into it his memories and wishes. Is that not real?
Cobb had the same catharsis. He dreamt-- four levels down-- a catharsis with his wife that never actually happened "in real life." But that doesn't matter, not for Cobb or his kids.
What makes the film so perplexing is precisely the ambiguity necessary to get across the point about simulation. If the narrative clearly identified totems, who was dreaming, and how many levels down we were, it would be clear to us the audience the difference between simulation and reality. But that's not the point of the narrative, indeed, it tries to frustrate that inclination. The point is catharsis.
The problem with making the distinction "dream vs. not dream" is that it fails to get you off the staircase. It's debatable, but probably likely, that Cobb was on the phone with his kids in real life, and dreaming when with Ariadne in the cafe. But why should we believe that he's wanted for his wife's murder? And that a Japanese tycoon can alter a gigantic criminal justice bureaucracy with a ten second phone call? Why doesn't he just move his kids out to Paris? It's more plausible that "the police want to get me" is a projection of his guilt; I can't go home...I can't face my kids... Looked at from this perspective, what's dream and what's not is irrelevant to Cobb. If it matters to you, that's your own baggage.
You want to know what's real? His wife is still dead. That's real, very real, everything else in the world, no matter how real, is less real than that. But they had their time together, (however brief and incomplete it may have been in real life, however sudden and savage and wrong was her death.)
It's time to let her go.
What's keeping you on the staircase is the fear that getting off the staircase means you'll never see her again.
In the warehouse, Cobb explains that Mal was possessed "by the idea that their world wasn't real." Adriadne tries to comfort him: "you're not responsible for the idea that killed her." But of course he thinks he was. He implanted that idea into her head in their 50 year dream life, she lay on the tracks with him so they could die/wake up, but that idea stuck into her real life-- so she jumped from a building. That event gave him his guilt. It is irrelevant whether her jumping happened in a dream or in real life-- he still carried a guilt around with him.
The top isn't the totem, and the wedding ring isn't his totem. The totem is his guilt-- "this is my fault." It is his origin. It is his inception.
He incepted himself.
Miscellany: many trains, Kyoto, freight train in the street, Cobb and Mal's suicide train, the train underneath the moving bridge which Yusuf drives off. Train is a common metaphor for thought, one track mind, train of thought, get back on track.
Water: stream of consciousness, put under, sleep deeply. Symbol of the unconscious: fear death by water.
If you're busy looking for what's dream and what's not, you're just trapped running the staircase. You need to change the perspective.
Cobb has Fischer hostage in the warehouse; he tosses Eames disguised as Browning next to him and says, "you have one hour!" (to figure out "the combination" to the safe.) Exactly one hour later (yes, I timed it), Fischer and the real Browning escape from the submerged van and swim to the shore, where Fischer proclaims he will break up the company. Yay, the plan worked, inception worked.
But if that dream time matches our (the audience's) real time, then are we dreaming?
Inception is also an allegory of filmmaking or narrative construction. It's a movie about it's own making. It describes how the simulation (movie) is constructed and manipulated so as to become the reality.
So change the perspective. Forget about the top, forget about the ring, look elsewhere. The children are wearing black shoes throughout the movie, until the final scene where they are wearing white sneakers.
But be careful, that doesn't tell you what's dream and what's not, it tells you that they have changed. That's what's important. It may be a dream or it may be real, but they are now different-- they aren't a memory.
Others have observed that in imdb, the children are played by two pairs of actors, two years apart. In a movie about narrative structure, are we supposed to ignore the structure of that movie?
("We have to buy out the cabin... and the first class flight attendant." I know just the gal; and I'll throw in a kid, for free.)
So either he is truly awake at the end and about two years have passed since Mal's death; or he's still asleep, but has moved past staricasing memories and moved into new dreamspace. It doesn't matter to Cobb.
What matters isn't whether the top stopped spinning; what matters is that Cobb didn't bother to find out.
(special thanks to pastabagel for his perspective)