I believe it's up to each person's personal perception. You could easily take the ending in two ways. One he survived moving the bomb, got married to Catwoman and has been fine. This leaving what he had left to Robin. The other way I believe you can interpret the ending is as follows: in The Dark Knight Harvey Dent said, " You either die a hero or live long enough to see yourself become the villain". This meaning that after Dent's death was blamed on Batman he became the villain. At the end of The Dark Knight Rises Batman could have sacrificed his life to save Gotham, thus dying a hero. Those are my two interpretations.
I believe what Batman did was ejected himself from The Bat (which is his giant flying thing) if you notice earlier in the movie he says he fixed the ejection seat. So I believe he is alive and married to Selena Kyle (Catwoman).
There is a scene in the movie where Alfred pours his heart out to Batman telling him what he would wish for Batman's future...a quiet life with a family living abroad in peace and WITH inner peace. I took it to mean he is still alive because of the surprise and happiness that was shown on Alfred's face when he saw Batman again in the outdoor cafe.