What is the most interesting part of Oliver Twist?

The most interesting part of the story is when Sikes murders Nancy.

The most interesting part of any book might be in the eye of the beholder.  There are certainly many interesting parts of the story, such as when Oliver asked for more gruel, when he became apprenticed to an undertaker, or when Fagin took him in to try to teach him to be a criminal.  Oliver’s arrest, kidnapping, and attempted burglary are all also very exciting.  However, I have always found the part where Bill Sikes kills Nancy to be especially important.

Sikes was abusive to Nancy, there is no question about it.  She was also kind to Oliver, and few of the criminals were.  For this reason, Nancy ended up dead.  Dickens foreshadows this when Sikes forces Nancy to go and get Oliver after Brownlow rescues him.  Nancy refuses to go until Sikes forces her to.

By dint of alternate threats, promises, and bribes, the lady in question was ultimately prevailed upon to undertake the commission. She was not, indeed, withheld by the same considerations as her agreeable friend; for … she was not under the same apprehension of being recognised by any of her numerous acquaintances. (Ch. 13)

Nancy goes so far as to talk to Rose Maylie and Brownlow to tell them what happened to Oliver and his life story.  Nancy is aware that Oliver is not like the other boys.  All of Fagin’s attempts to get Oliver to turn into a criminal have failed.  She wants to rescue him from a life of crime.

She staggered and fell: nearly blinded with the blood that rained down from a deep gash in her forehead; but raising herself, with difficulty, on her knees, drew from her bosom a white handkerchief—Rose Maylie's own … (Ch. 48)

Sikes kills Nancy because he thinks she told on all of them to Brownloaw and to the police.  Since she was followed to her meeting on the bridge, he thinks that she betrayed them, and for this reason he kills her.

Due to Nancy's sacrifice, Oliver is able to live with his new family and does not have to succumb to a life of crime.  Leeford's efforts to make him a criminal have failed, and Oliver remained good.