One of my favourite books is Black Beauty by Anna Sewell - I read it as a child and still have a copy on my bookshelf to go back to every so often.
Haven't read this for years. I too also like to reread favourite books. I have had to replace my copy of Lord of the Rings as it fell to pieces due to overuse. The first time of reading you get caught up in the story but subsequent readings allow you to see the characters better.