Although no one can prove it one way or another, unless that person is Chris Nolan, it is hard to say. Both theories are possible.
Evidence to Reality: If we accept that the entire movie is not a dream, and that Cobb did in fact escape his limbo with Mal, then it is reasonable to believe he also escaped his limbo with Saito. Also, there are simple explanations as to why when he sees his kids again they look much like they did in his dream. For example, he never saw his kids faces so we cannot easily tell if they had aged much from his memory. In addition, the movie never defines the amount of time that has passed since Mal had died and Cobb was banned from the U.S. So the memory of his kids may only be a few months old, therefore it is very possible his kids look pretty much the same in the memories and in the present. In addition, the visual duration of the top spinning is never a trustworthy totem at all, since it is a property of the totem others can observe and recreate. If the top is to be trustworthy at all, it is Cobb's knowledge of how it feels to spin it that convinces him he is awake, not the duration of the spinning, which we can presume will end eventually in the final scene. Visually, there is an obvious difference between the wobbly spinning in the end-scene and the absolutely perfect spin in the safe during limbo, again implying the possibility that the final spin could be natural (though only the feel in Cobb's fingers would know for sure). It is alleged that at the end of the film Cobb's children are wearing different, albeit similar clothing compared to the clothes they wear in Cobb's subconscious. In the opening scene dream, you get a glimpse of Cobb's hand. He's wearing his wedding ring. Now, if you follow the rest of the movie keeping an eye out for this you will notice that he only has the ring on when he's allegedly in a dream. At the end of the movie he isn't wearing the ring. If the ring only appears when he's in a dream and he's not wearing at the end of the film, that could be confirmation that in fact he woke up.
Evidence to Dream: It is possible that the entire movie is a dream, and that Cobb never left his own limbo. The children appear the same age as in a previous memory, and in fact, appear to have the same motions and same clothes in the yard before turning around. It suggests to the viewer that this is exactly the same as his memory, and thus he could be still dreaming. How long the top spins is not a good totem, except in that it spinning forever is only possible in the dream world. A short-duration spin is a visual property that someone could easily recreate in a dream. If we trust the spinning top, it must be the exact feel in Cobb's fingers as he spins it that convinces him it is genuine. However, Cobb admits that the totem was originally Mal's totem, suggesting that he adopted it as his totem during limbo, making it impossible for him to know the true feel. In addition, a totem can not prove that you've woken up from your own dream, since you know it's true 'feel' and thus your subconscious can recreate it properly.[/spoiler]
Also: This may be a continutity error, but when Arthur comes to get Cobb in Tokyo, they leave the hotel room and go to the roof for the helicopter at night. When they're on the roof, it's day.
"Both theories are true" theory: Movie has two main themes: the first one is that the line between dreams and reality can be imperceptible from the perspective of an individual; the second that an idea can be a parasite which, once incepted, can take over one's psyche. The ending simply reflects the fact that the idea that killed Mal has now taken over Cobb; he cannot discern whether he is now living in a dream or a reality, and we, the audience, witness that intimately. The gyro in the end falters, but we do not see whether it stops or not. Have we witnessed it stop, the movie would be essentially telling us "fear not, this is real and a happy end". Had the shot ended with it spinning, the movie would affirm the other theory. However, the shot as-is wants to ensure us that we do not know and we cannot know, because Cobb doesn't know anymore. The lack of definite answer IS the answer; for the rest of his life Cobb will wonder whether everything around him is real, and the audience is deliberately left with that same question hanging in their heads. Notice that when Cobb is in his "Memory bank" with Ariadne, Cobb is looking out the window at his kids, he tells Ariadne that his greatest regret is not being able to alter this moment and see his children's beautiful faces again. That would imply that was Cobb's inception to himself. He finally did what he could never do before and altered the moment in which he saw his children and he sees their faces. Also, why was Miles there? He was living in France yet was waiting at the airport in the States (reason why MIles was there: When Cobb visitied Miles it was to give him a gift for his children. i.e. Miles was traveling to see Cobb's children in the near future, and obviously Cobb could and would have made arrangements with Miles when he knew he was coming back to America). Even more confusing, Miles' wife, Mal's mother was taking care of Cobb's children in America yet we never see her at the house at the end . The inception itself could be altering his biggest regrets which spreads to every aspect of his life he winds up needing to alter. Or Mal was right the whole time and he was actually still down one dream level and Mal is alive in reality and Cobb wasn't waking up.
The Spiritual / Metaphysical explanation: From a spiritual perspective there is a different reading again. This movie is one with a profound spiritual idea at its heart, for those interested - just as with 'The Matrix', and Guy Ritchie's 'Revolver'. In 'Inception', Nolan seems to be using the metaphysics given in 'A Course In Miracles', a seminal spiritual text from the 1970s that was purportedly channelled from Jesus and which continues to profoundly influence modern spiritual thinking. In ACIM the key idea is that what we think of as reality is in fact a dream - that there is no difference between the dreams we see at night, and what we see with our eyes open. Both are projections of our mind, which is trying to escape a core guilt by projecting guilt outside of itself onto projected 'dream figures'. [spoiler](For more on this see the FAQ titled 'If the spinning top really did keep spinning at the end...'). Thus, although Cobb returned to 'reality', Nolan seems to be making the point that what we think of as 'reality' is still a dream. And, that within that dream, we see what we want to see - projection makes perception. Thus, the movie is devised so that some viewers look at the spinning top and see it as being about to fall over as the movie ends. They decide that the movie is saying that Cobb is back in 'reality' and not dreaming. Others see the top as going to continue spinning indefinitely. But, one then inevitably asks, how could Cobb be still in a dream? Which leads us to think hard, to debate, to share ideas, and perhaps eventually to question the unquestionable - that 'reality' is not what it seems to be. Nolan is cleverly sowing a key idea in our consciousness. So you could say the movie Inception is in itself... an inception! Within this interpretative framework, Nolan is reaching to us within the 'dream' that we call reality to help us to start to challenge our assumptions about 'reality' and begin to wake up - just as Cobb went into limbo to get Saito.
Yet for an inception to work, one must accept it as one's own thought process... so of course Nolan does not give interviews where he says, 'This is a movie where I'm trying to wake people up to the fact that they're dreaming'.