Everyone gets together, at a cafe or a bookstore or some public place,
and they bring a few books with them, and mingle with people, and
explain why they like those books, and people swap books.

You can make it kind of game-like.  People have to register so they can
get in contact with their lendee.  Think eBay reputation management.
The sponsoring organization, say Amazon.com, can offer Internet kiosks
where you can add books to your wish list.