I know that I seriously dropped the ball on this feature leading up to The Dark Knight. Though I may not be able to cover all of Batman's Rogues Gallery, I figure I can still hit the high points.
Two-Face has been a staple villain for the Batman since his first appearance in 1942. Two-Face was once Harvey Dent, District Attorney of Gotham City and an ally of Batman. After a criminal disfigured half of his face with acid, Dent became the insane crime boss Two-Face, who chose to do either good or evil depending upon the results of flipping a coin. He was partly inspired by the dual personality of the character Dr. Jekyll and Mr. Hyde.
Originally, Two-Face was a many gimmick-focused comic book villains, plotting crimes based around the number two, such as robbing Gotham Second National Bank at 2:00 on February 2. In recent years, writers have portrayed his obsession with duality and fate and his criminal behavior as the result of multiple personality disorder and a history of child abuse. He obsessively makes all important decisions by flipping a two-headed coin, one side of which is scratched over with an X. The fact that Dent was formerly a friend of Bruce Wayne and an ally of Batman before his scarring colored their now adversarial relationship is also a more prominent element in modern stories.
The character of Harvey Dent was played by none other than Lando Calrissian's Billy Dee Williams in 1989's Batman. In Batman Forever the role went to Tommy Lee Jones who was already transformed into Two Face. Most recently, he was played by Aaron Eckhart in The Dark Knight. Though Two-Face appeared in Batman: The Animated Series, he has a couple of notable omissions from The Batman and the 1960's series.
Throughout his history, Two-Face's face has been surgicacally repaired any number of times, but his mind remains damged and ultimately he tends to redamge his face to match.