EW are holding a 'Book Swap Week' at our regular coffee mornings in the second week of September, have a look:
http://www.expatwoman.com/dubai/monthly_things_to_do_EW_Book_Swap_Week_11526.aspx
Not only can you donate your second hand books but you can get some new reads in return - perfect!
Maybe think about selling the most current ones/hardbacks to House of Prose in the Dubai Garden Ctr on SZR near Gold & Diamond Park for a little spare cash and then donating the rest to a charity like K9 -- they sell them to raise funds.
rhubard: I would be interested in taking your books, I'm a bookworm :-) if you could post a vague list of what you have I would happily go and collect.
Not sure if this is the type of thing you're looking for, but the MORE cafes in at least the DIFC and the Gold & Diamond Park run an informal book exchange. It's a "leave a book, take a book" type of thing, but I'm sure they would take a load of books off your hands as well.