Christopher Nolan loves messing with his audience, so he's left it deliberately difficult for you to work out what's going on! There's no definite answer to your question, only theories and speculations. Here's what I think:
Inception Ends With Cobb (DiCaprio) Back In The Real World
Like I said before, there are no definitive answers, but here's why I believe Cobb has returned to reality.
- His totem, the spinning top, wobbles in the final scene. It doesn't stop spinning, as the film ends before it has a chance to, but the top never wobbles in the dream-world.
- Cobb's children are played by four actors - although they may look similar at the beginning and at the end, they're actually two or three years older by the end of the movie, and are played by different actors.
However, I'm not totally convinced that 'is he dreaming?' is really the question that Nolan's trying to leave you with. I think it's about reality - if something seems real, feels real, and your mind tells you it's real, does it matter if it's not actually real?
Cobb's happy - even if it turns out he is stuck in limbo, he's still much more content than he was before - so does it matter?
Nolan is making you question the nature of reality, and that's why the movie messes with your head. Everybody's reality is different, and there's no way of knowing what's real and what isn't - we can only rely on our senses, but as we all know, dreams can be so vivid that they seem perfectly real at the time.
Screenrant has a brilliant article explaining Inception - not just the ending, but all the other bits that get confusing. I'd recommend reading that over if you're still unsure!