If I were to pick one piece of literature that has affected me deeply, it would be The Hobbit by J. R. R. Tolkien.
Now, I don't read very much in my free time, and what I read might not be considered actual literature, being mostly fictional novels for young adults. But one week I was stuck in a auto body shop with my father and I had aught else to do, and I picked up The Hobbit to pass the time, and all I wanted to do while I was reading it was to keep reading it, even up until it was time to leave and continue our business. But all I wanted to do was stay in Tolkien's fantastic world for a little while longer.
That is the only time I would say that a piece of literature has affected me so much.