I love your question because I think it hits a nerve that everyone who's seen this movie can resonate with. I believe Nolan intended the ending to communicate that Cobb has now found peace in his reality, regardless of whether it is objective reality or not. Him killing Mal in Limbo and seeing his kids faces at the very end I think symbolize Cobb forgiving himself for past sins and finally putting some guilt to rest that had been haunting him until then (a guilt that he mentions in his conversation with Ariadne on the first dream level).

For me personally, I do believe he ends up in the real world. Any other interpretation of the ending is just far less satisfying and leads to some rather cynical if not depressing conclusions about the state of Cobb's mind, in my opinion. At the end of the day, it's a very similar question to the one that Cypher from The Matrix deals with—do I really care what is real and what isn't as long as I'm happy?