Bookmooch is an online trading community for books. You get points for giving away books and you can recoup the points to receive books from others. I emailed them to ask how public libraries could take advantage of the site. Here is the reply:
1) by participating, ie getting rid of the books they no longer want in order to earn points, which they could use to get free books they'd otherwise buy
2) as a charitable cause: I have a small number of points received to the "library fund" http://bookmooch.com/charity as donations that I can give out to public libraries. This is not big yet (we've been up only two weeks) and is around 10 book points.
If you are weeding, you might want to take a look at this site as an optional way to discard your books and get something in return.