Nolan intends for people to be guessing, and he's unlikely to ever say which interpretation is correct (great artists know it's best to leave things like that ambiguous, to keep people talking), so to me it comes down to which interpretation you think makes the most sense for the movie.
I'll start by saying that I discount the various theories about how the whole movie was a dream or some kind of elaborate alternate inception, etc., because you really can't argue about that either way and it would sort of make the whole thing pointless. I focus solely on whether he woke up or not at the end.
I would say he did, simply because I think it's much more consistent with Cobb's character arc leading up to it; for most of the movie, he's descending, he has the big climactic confrontation with Mal, and the point of his rejection of her and his speech about it is that he recognizes that she's not real and refuses to accept dreams. To have him then turn around and fall into a dream kind of voids his whole character arc.