It isn't just the ending of Inception that's ambiguous. Virtually every scene has you questioning what's real and what isn't as Christopher Nolan went out of his way to boggle the audience's collective mind with his dream-within-a-dream concept.
The final scene sees Leonardo DiCaprio's Dom Cobb reunited with his children at his father's house, having seemingly escaped limbo. He sets his 'Totem' - a spinning top he uses to establish dream from reality - in motion and turns his back on it. In the movie's final shot, the top stutters ever so slightly before the credits start to roll.
Many fans left the theatre fixated on whether the top was about to buckle over, revealing that Cobb was in the real world, or continue to spin and confirm the reunion was just another of the protagonist's dream. There have even been fan theories claiming that Cobb's wedding ring, and not the top, is actually his 'Totem'.
Although this discussion is healthy and can be stimulating, it's also unnecessary, because the take-home point from Inception's final scene is that Cobb didn't care whether the top would continue to spin. At that moment, he was happy.
Inception is keen to stress the value of dreams as personal and meaningful experiences, so in the context of the movie, it was irrelevant whether Cobb was with his children in the waking world or elsewhere.