What happened at the end of Inception? What's the truth behind the spinning top?

Did the spinning top fall at the end of Inception? If so, what did that indicate?

Oh, yesssss... I've been waiting to come across this question on Quora. And having watched the movie about 40 times, I suppose it makes me something of an authority on this topic.

So, which is it? Is he still dreaming or not?
Let's find out. (I couldn't resist using the three step reveal used in The Prestige so bear with me.)

"Now you're looking for the secret... but you won't find it, because of course you're not really looking. You don't really want to know. You want to be fooled."
- Cutter (from The Prestige)

This answer is based on facts accepted at their face value — that the story begins from a reality. (i.e The Cobol Job)

The Pledge: Since Cobb keeps using the spinning top in his dreams, we assume that the top is what we have to keep a close eye on, by default. And that's okay. It behaves just like it is supposed to —keeps spinning when he's dreaming and topples when he's not. But it doesn't get you any closer to understanding what happens in the end.

The Turn: So, how do we find out if Cobb's dreaming in the end? When Ariadne enters Cobb's dream when he's carrying out "experiments"

Important? Very...!!

Why? Because that means, in each and every of Cobb's dreams, he should be wearing his wedding ring.

That is what will help us decipher what happens the end — not the spinning top.

The Prestige: "Okay, how?" you ask me. I say "He's seen wearing his ring in every dream. That's right."

1. Yusuf's dream

2. Arthur's dream

3. Eames' dream

(I know it's a bit blurry, but the ring is there.)

4. Saito's Limbo

BUT a few minutes before spinning his top at his home dining table, back at the airport.

And that means it doesn't matter that we don't get to see if the top topples in the end or not.

Cobb is NOT dreaming in the end.

I realize you may think, "What about his kids? They're wearing the same clothes."

No they're not.

This is what they're wearing when his subconscious intrudes into his other dreams.

And this is what they're wearing when he gets back home.

Also there are two sets of children cast in the movie. 3 year old Phillipa and 20 months old James & 5 year old Phillipa and 3 year old James. Check the end credits.

UPDATE: (I'm posting an update here so that all future readers fully understand the implications of the question.)

After an engaging conversation with Mark Hughes, (check comments below) I've decided to make this a part of my answer so that all possible questions are answered in advance.

There's no doubt that Inception is one of the most skillfully fabricated stories of our time with an equally surprising/ambiguous conclusion. As expected, everyone had their own versions of "Whether Cobb was dreaming or not." And most were quite convincing. However, in a public meeting, when questioned about the ending, Christopher Nolan discarded most theories, including the one mentioned above. So what are we to make of it?

THAT THE ENDING DOESN'T MATTER...!!

We're so hung up on details that we forget the most important aspects of our lives. And we did the same with the ending of this great story. We are so intent on figuring out the exact events that follow after Cobb returns home, that we don't notice the actual moral of all this. Cobb chooses not to question his reality — he lets go and embraces his children, he chooses happiness.

Of all the theories that were discarded by Christopher Nolan that day, he did not reject one of them — the theory that the entire movie is a dream, that we are the subjects. That the idea was planted in our minds. You see, Cobb's is an unreliable point of view. We're not even sure if his "waking" scenes are real. But in the end, he simply doesn't care about the reality of it!

(Which is exactly what we did. Just like Cobb, we chose the ending that made us happy — that he wasn't dreaming in the end.)

THAT was the intent behind the last scene. It isn't ambiguous, it isn't unresolved. It's just convenient — to each his own ending.