Many people have asked the question; HOW DID THE JOKER GET HIS SCARS/SMILE? This is my explanation, giving all of the information I know and remember right now. If I remember - or learn - any further information, I'll add it to the bottom of this post.
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There were many different stories. In the original Batman movie which starred Jack Nicholson as the Joker, we see the villain Jack Napier fall into a vat of acid. His face is disfigured, and the plastic surgeon he goes to says that not much can be done. After the acid followed by the surgery, his face is left permanently white and shaped in a huge grin, his lips red, and his hair green and greasy. Jack Napier, as it is, was also the gangster who killed Bruce Wayne's parents when he was younger, and nearly killed Bruce himself before sirens in the background chased the villain away. The famous line from this scene (and my favorite quote) was said by Napier as he aimed his gun at young Wayne's head, "Have you ever danced with the devil in the pale moonlight?".

In the new movie, The Dark Knight, there were several stories explaining the scars on the Jokers face. He himself cannot remember. Whether he makes up these stories to intimidate others is unknown, but he does believe them himself. If he knowingly makes it up, I believe it is to deteriorate the belief of good in all people (the first story, his father cut open his face: abusive father, bad family, etc; the second story, he cut his own face open because he loved his wife and she left him because he was ugly: selfishness, judgementalism, etc). Whether he knowingly makes them up or not, the fact that he himself cannot remember the truth is to show and highlight his insanity.
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