It's a bit ambiguous as to whether Bruce Wayne dies and to whether Batman Dies.
A1) Batman Lives, Bruce dies.
This is the theory I subscribe to. Earlier in the series the reason Rachel chooses Harvey is that Bruce will always put the city of Gotham above everything, and so after the psychological torment he's gone through he can't do that anymore, and knows that as long as he lives he'll have to. Alfred says earlier that he often imagines exactly the scene at the end of TDKR, so it seems likely that it's in his head. And for it to be real, Batman would have had to go up to Catwoman and say something to the effect of "Hey, want to go to the same cafe in Italy every day for a few months and wait for my butler?" Batman lives through Joseph Gordon Levitt.
A2) Bruce dies, Batman dies.
Same as above, but JGL doesn't become Batman. Maybe he's Robin, something else, or nothing. Ben Affleck is the next Batman, so I guess we'll never know if JGL was supposed to succeed Bale as the Dark Knight.
B1) Bruce Lives, Batman dies.
We see late in the movie that the auto-pilot was fixed. Those who think Bruce lived point to this as how he escaped. I think it is just to establish his psychological state, in showing that he had a choice but still sacrificed himself. And then no more Batman as explained above.
B2) Both Live. Not likely