The pure nature of the Joker, especially in the movie sense, is to be completely chaotic wanting "to watch the world burn". In other words, the Joker is the very definition of the alignment: Chaotic Evil
In the movie, the conflicting stories about his past are there on purpose to continue this nature of just being an agent of chaos.
Notice how we're never given a flashback of events during his story-telling, something very prominent in the movies in order to remind the audience of events past. Even Ra's' origins were given flashbacks, although brief and nondescript.
The only facts to his backgrounds are that he started in Gotham, pitting low-level criminals against each other in elaborate robbery schemes where he comes out on top, with money.
As a point of reference, the opening scene of The Dark Knight shows his most recent attempt, with a lack of surprise from Gordon on the situation of criminals killing each other during a heist.
But this is only the past year (time between the end of Batman Begins and the beginning of The Dark Knight) and the rest of his timeline is what we see in the movie.
For clarification and emphasis of the answer:
There is no true origin of the Joker in any media.
As far as the comics, the same is true:
There are a multitude of origins of the Joker told from being a washed up comedian that went nuts, to just being that way from the start.
Though many have been related, a definitive history of the Joker has never been established in the comics, and his true name has never been confirmed.
No recounting of the Joker's origin has been definitive, however, as he has been portrayed as lying so often about his former life that he himself is confused as to what actually happened. As he says in The Killing Joke: "Sometimes I remember it one way, sometimes another... if I'm going to have a past, I prefer it to be multiple choice!"
The one true constant of any depiction of the Joker is that he wants to assert to Batman that all it takes is One bad day to send anyone into the insanity that he lives everyday.
The most prominent of this is during the short story The Killing Joke where he tortures Gordon almost to this point.
And this is also what makes the Joker such the notorious villain that he is. No one can ever be certain of anything of him or what he will do. Whether it be something as simplistic as his background to any of his plans, constantly fooling even the pinnacle of detectives like Batman on multiple occasions.
As a final side note about Joker origin, the story that is most accepted as the "true" origin is The Killing Joke Where he quits his job to be a comedian and goes completely nuts after being knocked into a vat of acid that bleaches his body the traditional Joker colours (all caused by Batman during a heist gone wrong).
But as there is no confirmation of this origin to the Joker, even this can be taken with a grain of salt.
The Dark Knight's interpretation of the Joker is based primarily on the character's first two appearances in the Batman comics, as well as Alan Moore's one-shot comic book Batman: The Killing Joke, which was given to Heath Ledger in order to prepare for his role.