Gotham General Hospital is one of the largest hospitals in Gotham City.
The Dark Knight
Harvey Dent was taken to this hospital after having half of his face horribly scarred, thus making the place a target for the Joker to blow up if Coleman Reese, who was planning to reveal Batman's true identity to the city on TV, wasn't killed by any of the other patients' reletives within an hour. During the hospital's evacuation at the time, the Joker snuck in disguised as a nurse to meet with Dent, who has been raging over the death of his fiancee Rachel Dawes, and convince him to seek revenge through anarchy. The hospital was finally destroyed by the clown during both his and Dent's departures, in which the Joker took a bus-load of hostages, among them reporter Mike Engel.
The Dark Knight Rises
About eight years later, the hospital was rebuilt, and James Gordon was taken to it after getting wounded by Bane's henchmen. When Bane subsequently took over the city, some of his men invaded the hospital to either kidnap or assassinate Gordon, but the police commissioner managed to stop them and escaped with the assistance of John Blake.