While the question as to what act of violence is most shocking is a subjective one that will vary from reader to reader, since Oliver Twist's publication most readers seem to have been most disturbed by the murder of Nancy.
Nancy is perhaps the most complicated character in the novel. She is a thief and prostitute who initially works with Fagin and the rest of the gang to keep Oliver in the criminal underworld. However, she starts to pity Oliver and appreciate his innocence, perhaps seeing in Oliver the innocent child she once was before she was corrupted by criminal adults around her. She tries to save Oliver, and for her trouble, she is murdered by her lover Bill Sikes.
In the light of her character development and her own affection for Bill, the scene of her murder is nightmarish. Dragged from bed and only half-dressed, Nancy is beaten, first with a pistol, then with a club: a forehead wound bleeds so much that Nancy is "blinded" with her own blood before she is killed.
Dickens was accused of reveling in sensational violence during this scene. However, Dickens based this murder on the real-life killing of a prostitute named Eliza Grimwood, whose body was similarly brutalized by her killer. Oliver Twist as a whole was seen as shocking and gritty in its time, and Nancy's murder was no different. It absolutely fits in the novel because it serves many different purposes: first, it accurately depicts the brutality in the criminal underworld, particularly the brutality suffered by sex workers, and second, it shows what world Oliver is escaping from. Seeing the brutality and danger surrounding him increases the stakes and suspense of his escape.
Nancy's death is tragic and Oliver is probably too young to appreciate the enormity of her sacrifice himself, but the reader likely is not. Nancy's death turns her into an unusual Christ symbol since she dies protecting Oliver. Ultimately, the scene is tragic, showing how Nancy was ultimately destroyed by the criminal world. After her murder, Bill becomes tortured with guilt.