Great Expectations utilizes many adaptations of fairy tale archetypes: an innocent child (Pip, when we first meet him); a monstrous ogre (of sorts) who threatens to eat him (Magwitch, when we first meet him); a witch type who casts spells over people (Miss Havisham); and even an evil stepmother, although in this case, that role is played by Pip's sister.
Also, as in some fairy tales, there is an act of kindness that has many unexpected consequences. Pip undergoes a sort of Cinderella-like transformation, but unlike Cinderella, who retains her essential compassionate nature, Pip has to learn what is really valuable in life through the plot's twists and unexpected reveals.
In the end, however, Dickens does fall prey to what I think is his one fault as a novelist: a tendency to sentimentality. It's highly unlikely that Estella, raised as she is to be totally unfeeling, would undergo the transformation Dickens gives her so that she can return Pip's love. That is, perhaps, a real "fairy tale...
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