I've re-read a lot of books, all for basically the same reasons. There's a combination of factors at work, but mostly because I can relate to the main character. However, no matter what that characters trials and tribulations are, the scenery and background has to be rich, or I get bored quickly. When an author creates authentic surroundings with rich prose and imagination, I can't get enough of it.
Some examples are of course, LOTR as Tolkien is the master when it comes to layers upon layers of characters and places that wow the imagination, but for me, LOTR is all about Frodo. I can really relate to the little guy and his quest to destroy the ring. I've experience a similar task, even if, for me, the ring is merely symbolic for a particular challenge I've dealt with my whole life. Beyond that, all the other races - I'm especially fond of the Ents - represent different facets of humanity for me, though I don't know if that was Tolkien's intent, I'd like to think so, anyway. Another is the Clan of the Cave Bear series by Jean Auel, Ayla of course being the central character whom again, I can relate to on a deep emotional level, but also the beautiful descriptions of her ancient world and her resourcefulness in it.
Less well known examples are In Country by Bobbie Ann Mason. I relate very well to Emmett Smith and his troubles trying to return to the world after Vietnam, and in the end, accepting life on life's terms because that's really all he can do, and I think he does it with grace and courage like no other character I've ever read. Ms. Mason paints the American south in the 1980's very realistically, I think.
Also, there's a whole series of books by "The Gears" as I call them. They are anthropologists who wrote (and still may be writing new ones, I'm not sure) a dozen or so books on Native American peoples which are novels, but are based on actual anthropological finds here in the US. People of the Lightning is my personal favorite because it was set in the same area of Florida I lived in for almost 12 years and it described the area perfectly. The research that goes into writing their books must be enormous, which makes me appreciate them that much more. Not only that, but they are again, well written with lots of descriptions of the setting in which the main characters live.
So, I guess for me, I re-read for a variety of reasons, but I think it boils to down to the main character and whether or not I can relate to their struggles. Books with main characters that are flouncy and shallow don't interest me in the least bit. There has to be a major challenge to overcome, or I get bored very fast. When the main character not only overcomes that challenge, or even better, challenges, but becomes a better person to boot, well, that's heaven for me and I find myself wanting to return to their world again and again - and do, relishing the experience.