I have read numerous books that I have considered to be "great books," but the thing about "great books" is that everyone has a different opinion of different books. I had to read "My Antonia" by Willa Cather in ninth grade; I did not like it at all, while my mother LOVED it. I suppose I didn't like it because it didn't have a plot that I liked -- in addition, I have things about non-contemporary plots. That same year, I had to read "The Joy Luck Club" by Amy Tan, which I absolutely loved, probably because of the original club, the writing, and its contemporary-ness.
To me, what makes a "great book" is an enthralling, interesting, ORIGINAL plot -- in the case of books that have plots that have been done before, I like a book that takes that plot, but takes it to another level. I wrote a short story about a closet gay living in a evangelical society. It's been done -- what people who read the story have told me is that they thought it was great because 1) I can relate, slightly, to the plot, minus the "evangelical" society, and, now, minus the fact of being a closet gay, and 2) because I took it to the next level, and went all out with the things the characters said. If a book has an unoriginal plot, but takes the story to a next level, and goes to the next level by adding MORE than just the plot, but adds subplots into it, that makes a "great book." In terms of original plots, the "greatest book" I've ever read was "Going Bovine" by Libba Bray, which had such an original, enthralling, saddening plot, but was so magical and just so farfetched that it could only come from the mind of someone who has the greatest concept of fantasy mixed with reality. And that was "Going Bovine," a tale of a teenage sufferer of mad cow disease, who goes on a cross-country journey with his dwarf roommate Gonzo to find a cure, and meets a talking lawn gnome, enemies, and legal trouble along the way. It was so original, and so sweet and saddening and so -- fantastic. It was and is, in my opinion, a "great book."
Another thing that makes a "great book" is a relatable character, but a relatable character who also is SO different than you. I like books where I can relate to the character. In my short story, the protagonist is a lot like me, but is SO different that he's so engaging, and so much fun to write about. If a character is EXACTLY like you, there's no point in continuing reading or writing the book. You need to be able to relate to the character, but there also needs to be something about the character that is different, and that is unlike you. It makes for an interesting character. Another thing about characters is that there needs to be fewer detail. Far too often, it seems that there is too much detail pertaining to the characters in stories. Sometimes it's good, but more often than not, you should be able to make your own mental image as to what the characters look like, and how they act, and what their traits are. A lot of books and short stories do this, and they're not all, in my opinion, "great books," but it's something that very well may contribute to my personal definition of a "great book."
All the best ♥