Date added: 2012/07/24
I do not recommend you read this if you have not yet seen the movie as it contains spoilers. I also advise that you rewatch Batman Begins before watching The Dark Knight Rises and you will know why after. The movie is a perfect conclusion to Batman Begins and closely related to the questions asked. You should ask yourself: will the day come when Gotham no longer needs Batman? Can he really inspire the people of Gotham? And can Bruce Wayne ever be happy?
Many people over the Internet are being led to believe Batman died and Alfred was only dreaming in the end. This however is NOT the case. Bruce Wayne starts a new life with Selina and I will explain why.
Many people have read online that it showed a scene where there were only 5 seconds left till the bomb would explode. But no one actually even saw if Batman was on the Bat at that time. It only showed the time and the aircraft. People are led to believe that Alfred was dreaming in the cafe scene at the end. It was not a dream and there is no link to Inception other than the fact that both movies are directed by the same person.
When Bruce takes Fox to where he parked the Bat (the new aircraft introduced in this movie), he mentions the autopilot is not working. Only after the bomb explodes does Fox find out from his engineers that Bruce had gotten the autopilot fixed already. Think, why would Christoper Nolan choose to show this scene in the end? Sometime before the bomb exploded, Bruce had turned on autopilot and ejected from the Bat. In the end, only the two veterans Fox and Alfred know he is still alive.
So why did Batman have to make everyone think he died along with the explosion? It's because the day that Gotham no longer needs Batman had already arrived. This question was brought up in all three of the movies. Together with Selina, Bruce started a new life by using the Clean Slate program to erase their records from all the databases in the world. A fresh life was what Selina was after and what Alfred wanted to see Bruce live onto.
Best quote I've heard for a long time - "A hero can be anyone. Even a man doing something as simple and reassuring as putting a coat around a young boy's shoulders to let him know the world hadn't ended." This is referring to how in Batman Begins, Gordon comforts Bruce Wayne after his parents had died by putting his coat around him.