First and foremost we should understand the concept of what had been done during the movie. The plan is not to extract or steal a dream but to implant a dream or rather an "idea" into Fisher's mind. Fisher is the heir of a corporation owner who their client wants to disown or destroy their company.
To accomplish this inception the plan is to use three levels of dream. The first level would appear as the "real world". In this first dream Fisher and his godfather were kidnapped and then he gave a code supposedly for a safe. Then they were drove into a van and supposedly made the second dream.
The second dream is in a hotel room where DiCaprio pretends as someone who wants to help Fisher. He informs him that someone is trying to steal something from his dream and he wants to help him. The only way to do this is for Fisher to enter his uncles dream and see the codes for himself.
Then, they entered into the third dream which is presented as an icy place where there are guards. At this stage DiCaprio or Cobb in the film sees her dead wife pulling the gun on Fisher, the girl who is the architect of the dream shot her wife. For Cobb to finally be free of his guilt, the two decided to enter a fourth dream stage.
During the fourth stage Cobb decided to remain in that dream level until he resolves what is hunting him. The van on the first level enters the water and signals the final kick to awaken them from their dream. The awakening begins as the dream world is destroyed one by one.
As the fourth level of dream is destroyed Cobb returns to the seen where he sees Saito and there he asked for the agreement to be honored and that both of them can return to reality, to which Saito agreed.
The ending seen sees Cobb awakening in the same plane with his companions seemingly happy that he did finally returned. He then returns to the United States and everything seems to be normal. As he reached home he was introduced back to his kids but before that Cobb decided to spin the totem but was distracted.
Many says that there is not enough time to judge whether the totem stopped spinning and fell or it continued to spin. If it fell then it was reality and if it did not it was a dream. The ending was very clear and there was no mistake to it.
Comparing the sequence where Cobb introduces the totem to the girl and the first time we saw him spinning the totem, the average time it took for the totem to fell was about 20 seconds. On the last scene of Inception, the total time the totem had been spinning was about 55 seconds and still ongoing.
THE CONCLUSION: Cobb is still in a dream and had not managed to wake up.