The way I see it, there's 3 ways Nolan's Batman films could end:
1. Nolan concludes his "theme": Kinda like how each Spiderman film tackled a variation of "with great power comes great responsibility", each of Nolan's Batman films is going to be built upon a theme (Batman Begins was all about "fear" and "purging fears". The Dark Knight is supposedly about "escalation" and Batman "losing himself to this monster he's created")....Nolan could have an over-all theme, which binds all three films together, and by concluding what he wants to say on the overarching theme could be a way Nolan could end his Batman trilogy.
2. A New Beginning: Like another poster wrote, Nolan's Batman "began" in Batman Begins, he perhaps "learns" in The Dark Knight, and perhaps he shall become "fully realized" in the third film. What I mean is Batman becomes the Batman we all know and love: he's full on badass, full on detective, full on amazing....he's not a rookie anymore....it's his third year, he's a pro, he's got Gotham on lock-down, he "cleaned up the streets". So the third film could end with Batman's success at "bringing Gotham back". If that happens, Batman 3 could end with Nolan ending the film with a new beginning, meaning Batman now has a new task, a new challenge, and the film ends with Batman realizing this and realizing "the battle continues", the film fades out, and thus ends Nolan's trilogy. The MOST OBVIOUS way Nolan can do this is by introducing Dick Grayson in the middle of the third Batman film and having the film end with Bruce realizing "Grayson will be trained, Grayson will be like me, he will be my protege" So Batman's story is somewhat fulfilled, but now he's taken on the task of training a partner, thus the film ends (Batman's a surrogate father....Dick is now the focus)
3. Warner Bros leaves it open for more sequels: Let's say The Dark Knight is a box office smash and Batman 3 earns even more money, you can bet Warner Bros is going to go the way of Spiderman and consider recasting everybody and keeping the series going with a new crew, or paying the actors and the crew a truck load of cash to keep the series going for a part 4, 5, 6 and so on. So that means Nolan's Batman 3 could end with NO DEFINITIVE CONCLUSION, meaning the film just ends....and it's left open for the Riddler to show up in part 4, Scarface in 5, and so on.
and that's the way I see it.
Greg