Ensemble Dark Horse: Miss Havisham is probably the most memorable character from the book, despite her supporting role. She even had a scientific phenomenon named after her - the Miss Havisham Effect, where a person suffers a painful longing for lost love.
Fan-Preferred Couple: The vast majority of readers want Pip and Estella to end up together. Even the adaptations swing heavily in this way. The revised ending, preferred by both Dickens and his friends, is the one used in modern printings of the book, while the original draft is sometimes included as an extra.
Pip and Herbert. Pip is very fond of Herbert, and Herbert refers to Pip as "my dear Handel", or "my dear boy" throughout the novel. Chapter 50 of the original text, when Herbert is tending to Pip's wounds, is swimming in this, especially at the end.
The way Herbert proposed to Pip to share his business with him and Clara just smelled of a threesome attempt that everyone would've agreed with.
Jerkass Woobie: Miss Havisham. After reading her backstory, her actions when it comes to raising Estella become understandable. And of course, Estella herself due to said upbringing.
The Scrappy: Most readers did not like Estella, finding her cold and haughty persona intolerable. There is an in-universe reason for it which makes her a little more sympathetic, but they also felt that Charles Dickens got really carried away with the descriptions of her beauty, and Pip pretty much falls for her based on her beauty alone even though she treats him with indifference at best. It was the 19th century where young men weren't able to socialize with women like they can now, but this comes across as shallow now. She does go through some Character Development that humbles her and makes her more friendly, but this happens at the very end. And off-screen.
Slow-Paced Beginning: The book takes a while to really get moving, despite a pretty action-packed first chapter. As a result of its serial nature, the first two parts rely heavily on building suspense that pays off in the third part (where nearly every chapter has a plot twist or revelation).