in our apartment building has lots of readers. what we do is put our books outside near the trash, but not in it. then whoever wants one of the books takes it. and because we have so many readers in this building, no book ever actually makes it into the trash. if they're missing the front cover or have worn out edges, we don't mind at all.
actually some of the other buildings near us do the same things, and that's how i found my mint hardcover w/dustjacket copy of "walt disney and assorted other characters" and some interesting detective fiction and biographies
or you can donate your books to the library. they usually sell them at book sales, so people who need cheap reading can find it, and the proceeds go to help the library
or perhaps a women's shelter, hospice or hospital could use the books even in worn condition.