Ledger Lives
Batman Begins (2005) - As IOTL
The Dark Knight (2008) - Close to IOTL, but the final fight with Gordon's kids taken hostage and such is with the Joker. Harvey doesn't lose his face or go crazy, but we do lose Rachel. Batman almost kills the Joker, but Gordon stops him.
The Caped Crusader (2010) - Focuses on the trial of the Joker; introduces Harley Quinn as the Joker's court appointed therapist (a small role, for now), Dent slowly goes crazy, and Batman is hunting a serial killer around Gotham. Batman frequently visits the Joker for insight on the killer kinda like Hannibal Lector or the Long Halloween. At some point the Joker scars Harvey and we discover that Harvey Dent is the serial killer - he's gone crazy. Batman takes responsibility for the Dent murders to save Harvey's reputation and the Joker case. The Joker is sentenced to the electric chair at the end of the movie.
The Dark Knight Falls (2012) - "You either die a hero or live long enough to see yourself become the villain". This is Batman as the villain as he is hunted by the GCPD which has replaced Jim Gordon (who's soft on Batman). A task force of new Commissioner Ellen Yindel, Officer John Blake, and FBI Agent Edward Nashton coordinate a hunt across Gotham. Nashton secretly releases the Scarecrow to draw Batman out, while Catwoman teases him and commits various robberies throughout the film. Nashton reveals the truth about Harvey Dent (he's a good investigator). At the end of the movie Bane appears seemingly out of nowhere; he was working with Nashton but now betrays him, breaks Batman, and takes over Gotham City. Also Selina betrays Bruce as well.
Gotham Rises (2014) - Covers Batman's rehabilitation as Gotham is split up: Scarecrow, Joker, Bane, and the GCPD all have their own sections of the city. It's fairly similar to the OTL movie / No Man's Land. Each person blames themself for what happened to Batman. Nashton cuts out his own swath of territory separate from the GCPD as he wants to wage direct war on Bane. Batman eventually returns to a Gotham which has proven that it still has heroes as Catwoman and the GCPD try to keep people safe. In the end the Joker appears and kills Bane ("You killed the Batman, that makes me very angry") instead of Selina Kyle doing it. Batman then subdues the Joker and the movie is over. At the end he offers to train John Blake - he's realized that his time as Batman is over.
An aside:
John Blake has a two movie arc through
Falls and
Rises. He takes various traits from the first three Robins. He starts out with more or less Jason Todd's personality and backstory - he grew up on the streets and is itching for a fight at least at first. Like Tim Drake he figures out Batman's secret identity but decides that he won't tell Nashton for the moment. He then spends most of Rises as sort of our focal character for Gotham City as he does stuff around the city, mellows out, and becomes a hero. By the end his personality has shifted more towards Dick Grayson as he loosens up and becomes jokey in battle.
Basically he's got Grayson's sense of humor, Jason's rage and desire to battle, and Tim's cunning and intelligence.