There are lots of interesting answers from authors from Pamela Sargent to N. K. Jemisin. You should go check out the whole thing. Meanwhile, here's a teaser in the form of my answer to the question:
If you'll bear with me, I'd like to answer this question a bit tangentially, by discussing my experience of rereading in general and then moving into the specific. Rereading is always interesting for me because of the way I was trained to read--namely, by my mother, who is a librarian, an avid reader, and someone who *hates* rereading.
To my mother, reading is accomplishing a task. It's checking off a box on your list of life's achievements. I have read that book--check.
Not that she doesn't enjoy reading. She loves reading. But to her, rereading is pointless. You've already checked off that box, so what's the point in revisiting?
So, then there's me. I love rereading, but I always feel a little guilty about it. It's kind of a guilty pleasure.
I tend to reread for one of three reasons:
I find the work extremely profound and revisiting it allows me to uncover new layers in the text. Not every work can tolerate this kind of rereading, but I love it when I find a text that is equally breathtaking--though usually breathtaking in a different way--on reread. I go to Octavia Butler's work for experiences like this, particularly Lilith's Brood and Parable of the Sower, although I admit it's gotten harder to do this since she died. As a friend of mine says, it's sad to live in a world where there will never be a new piece of work by Octavia Butler.
I find the work comforting and part of the reason I like rereading it is because it's a familiar, cozy experience. I reread many of the Terry Pratchett books every year or so. I often do it when I'm sick or stressed out and I don't have the mental resources to go exploring. I just want to be in a warm cocoon with Lions of Al Rassan or Doomsday Book or Wicked.
Nostalgia. I reread work because I want to evoke the feeling I had the first time I read it. This can be great--I really love Tanith Lee's Biting the Sun and Silver Metal Lover, for instance, although I think they were really something keyed into my experience of the world as an adolescent. Some children's books still have that crackle of a world I saw as potentially magical--E. L. Konigsburg's From the Mixed Up Files of Mrs. Basil E. Frankweiler, Roald Dahl's Mathilda, The Forbidden Door by Merilee Heyer. Rereading for nostalgia can also be painful, though. In college, when I met someone who had written Pern fan fiction in high school, I thought to myself, hey, it would be fun to read those again. "It really won't be," she told me, "You're going to be sad you did." I didn't believe her, but she was right and I was so very wrong.
Of course there's a lot of overlap between these categories. I find Octavia Butler's work very profound, but it also reminds me of all the times in all the previous years when I've read it before. Wicked is comforting, but also nostalgic of my adolescence--when I was sixteen, I painfully over-identified with Elphaba. Even though I see Biting the Sun through the eyes of my teenage self, I discover new layers when I reread it, too, especially as I read more feminist SF and gender theory and see the ways in which the book is part of an ongoing conversation.
I guess there's also a fourth reason I reread--which is when I'm trying to figure out how an author achieves a particular effect, or do a structural analysis on a text because I hope it will help me discover something about my own writing. But while I often end up doing this as I reread, I don't think it's usually what's on my mind when I go pick up the book. Instead I'll think "You know what I want to reread? That book!" and then when I'm halfway through, realize that it's because there was something in it that resonates with one of my own projects, or some way I'm thinking about writing, or even just a philosophical or emotional dilemma I've been contemplating.
I really love rereading--I find it inspirational, profound, comforting and nostalgic. But I have to admit, from time to time when I look at my shelves and see all the books I still haven't managed to pick up for the first time, I start to worry about all those empty boxes that I still can't check off.
--So, what books do you like to reread?