In Berlin exists a quite big sharing and exchange culture. If I have something I don’t need anymore, I usually put it on the mailbox with a note saying „zu verschenken“. Hardly ever something is not taken by someone. Books, Clothes and even furniture, somebody in the building could find a use for those things.
Another nice way to give books you have finished to someone else are the Public Book Cases. There is a list on Wikipedia with the addresses, I am sure there is one in your area.
This one is on the Seelingstraße 20, it is the one closest to my place. You can find every kind of book in there, in many languages (I saw, English, French, Italian, Turkish etc.).