Miss Havisham to Magwitch
Miss Havisham and Magwitch are similar in that both have amazing names, and both have protégés that they're prepping to enact some kind of revenge: Miss Havisham seeks revenge on men, and Magwitch seeks revenge on everyone who thought he was worthless. And both unintentionally wound the protégés for whom they work so hard to provide: Estella is incapable of love, and Pip almost loses everyone who loves him.
Estella to Biddy
Pip once tells Biddy that he wishes he could make himself fall in love with her, because he knows in his heart that she would be good for him. Biddy is wise, approachable, and generous of spirit. She is observant and is a good judge of character. She knows the power of self-determination and works her way to a position as a schoolmistress. Estella, by contrast, is lofty, cold, and uncaring. She does, however, give Pip sound advice (which is "don’t fall in love with me, or you’ll be sorry"). Both Biddy and Estella are orphans who have been raised by eccentric women and who survived some pretty horrible childhoods. They are strong, but their positions in society make them quite different women.
Pip to Herbert
Pip and Herbert are best friends—apparently because opposites attract:
Pip plays hard in London, and Herbert, if left to his own devices, would probably keep more to himself. Pip spends money like crazy, while Herbert chooses to live in rundown Barnwell's so that he doesn't have to rely on his father. Pip dreams of becoming a gentleman. Herbert, born into a family of some social standing, dreams of becoming a successful shipping merchant. Pip loves a woman who doesn't love him. Herbert loves a woman who adores him and who will marry him. Pip's dreams fail, but Herbert's dream succeeds (thanks to Pip's maneuvering). Pip often needs advice and help, while, luckily, Herbert is good at giving advice.
BFFs for life!
Compeyson to Drummle
Compeyson and Drummle are lovers and husbands (or almost-husbands) to Miss Havisham and Estella, respectively. Both men are cold, irreverent, and violent. Both men injure the women who love them. Both men meet their deaths in unusual ways: Compeyson drowns and Drummle is killed while mistreating a horse.