Can you describe Nancy's good character in Oliver Twist?

Nancy is first introduced into the narrative in Chapter IX when she and another young woman named Betsy, both of whom Dickens describes as “remarkably free and agreeable," drop in to have drinks as Fagin educates Oliver Twist in his lessons on how to pickpocket.  Nancy is further characterized as being the lover of the brutal Bill Sikes, exploited into being a prostitute and a thief.

But, after Nancy follows Fagin's instructions to find Oliver in order to learn the whereabouts of Mr. Brownlow, who takes Oliver in, she begins to have misgivings about her immoral life.  She, then, has ambiguous feelings regarding the capture of Oliver: should she disobey Fagin's order to find the boy and return him to a life of crime, or should she try to return Oliver to Fagin? Faced for the first time with a moral crisis, Nancy exhibits her intrinsically sterling character as she risks the deadly repercussions of trying to save Oliver from the dangerous life of crime in which she is involved.

In Chapter XVI, for instance, when Nancy returns Oliver to the thiefs, Sikes ridicules Oliver's fine clothing and even threatens to put his vicious dog upon the boy. Nancy leaps to little Oliver's defense,

'I don't care for that, Bill, I don't care for that,' screamed the girl, struggling violently with the man, 'the child shan't be torn down by the dog, unless you kill me first.'

Nancy loathes the idea that innocent Oliver be condemned to the derelict life that she has lived. Her spirit is, indeed, noble as she risks her own safety for the boy. For, when the angered Fagin attempts to hit Oliver with a club, Nancy intervenes, grabbing the club and flinging it into the fire with an abnormal strength. Of course, the cruel Sikes threatens Nancy with harm, but, she laughs, biting her lip so hard that blood is drawn. Later, in Chapter XX,

Oliver could see that he had some power over the girl's better feelings, and, for an instant, thought of appealing to her compassion for his helpless state.

That Nancy's environment and misfortunes in life play a role in forming her character are evinced in her conversation with Rose Maylie in Chapter XL:

When such as I, who have no certain roof but the coffin-lid, and no friend in sickness or death but the hospital nurse, set our rotten hearts on any man, and let him fill the place that has been a blank through all our wretched lives, who can hope to cure us?

However, both women, as counterpoints of one another in environment, demonstrate the compassion that is in the feminine heart. Nancy risks the wrath of Sikes and Fagin to save Oliver from the life she has to live as she meets Mr. Brownlow and Rose and reveals the story of Fagin, Sikes, and Monks, of whom Brownlow seems acquainted.  When Mr. Brownlow offers to help her, the tragic Nancy replies,  'I am chained to my old life. I loathe and hate it now, but I cannot leave it."  Her feelings prove to be well founded as Sikes, believing she has betrayed him and the others, brutally beats her to death.  Trapped in her environment, Nancy suffers as its victim.

Why should we admire Nancy in Oliver Twist? Provide three examples.

Nancy is an excellent character to analyse in this wonderful book of the Victorian underworld. I definitely think you are right to admire her, as your question states, and one of the principal reasons that you can use to justify your admiration is the way in which she is unique in the novel. The rest of the characters are marked by either being "good" or "bad" with no in-between states. Nancy, however, is a character that shows that in spite of the life she has had and the way that she has been corrupted by Bill Sikes and Fagin, she is still capable of nobility of thought, compassion and kindness.

This is most obviously shown in the way that she acts against Sikes and Fagin to try and save Oliver, and regrets her action in kidnapping him back into the world of crime in which she herself is mired. Note how she is described to us at the beginning of Chapter 40, when she meets with Miss Maylie:

The girl's life had been squandered in the streets and among the most noisome of the stews and dens of London, but there was something of the woman's original nature left in her still; and when she heard a light step approaching the door opposite to that by which she had entered and thought of the wide contrast which the small room would in another moment contain, she felt burdened with the sense of her own deep shame and shrunk as though she could scarecely bear the presence of her with whom she had sought this interview.

This, then, is why we admire Nancy: in spite of her corrupted upbringing and childhood, she still retains something of her "original nature." She feels shame at her state, and yet in spite of this, she acts against those who have power over her, even when she thinks it is likely she will be killed, to save Oliver from the same fate that has corrupted her.