I reread books because some of them just have to be read more than once.
Sometimes it is a comfort thing and often you get more out of a book second or third or twentieth time around because you are older, your life has changed and you can take something new away from it because you are ready for it now.
I get different things out of old favourites now I am older and have experienced different things in my life. They can completely change, sometimes I don't like them as much, sometimes I wonder how I could have missed something so important, sometimes I love them even more than before.
Books you love are like friends you love. Why would you only visit them once? If you love them, there's always something new to gain from returning to them.
I can't think of all the books I've reread because I love them but I'll put a few and try to give a reason for what I get out of them.
I love Stephen King's IT and The Stand and have reread both (and many of his others) often. I think there's something to learn from in both of them, and in fact most of his books have strong ethics and morals in them that rereading only helps to make clearer.
Jean Webb's Daddy Long Legs is lovely and is one of my comfort books.
The Lord of the Rings series has been one of my favourites for years, although on first reading it I hated it.
We Need To Talk About Kevin is very powerful and I think it's a must read, it deserves classic status.
Happenstance by Carol Shields has been a favourite for a long time. It's two books in one really, the story of the same five days told first from the wife's perspective and then from the husbands. Or vice versa, depending which side of the book you start from. My copy flips over so you can choose. I like The Republic of Love by the same author.
I reread The Slap, one of the most hated books ever I think, because even though I hated it the first time around, I couldn't stop thinking about it afterwards and I needed to read it again. I did get more out of it the second time and have kept it because I think I will read it again one day.
I like horror books best I think, so if something is well written and 'scares' me then I am likely to return to it. Discomfort reading can be just as good as comfort reading 
And if something is particularly funny then that's always good to go back to as well.