BookMooch is the Craigslist of swapping sites. It's not as fancy as some other sites (such as LaLa and Peerflix), but it's totally free to use. There's no monthly charge and no per-transaction fee. You do have to give to get, though: each book costs a point. You get one point for sending a book to a user, and a tenth of a point for each book you add to your Moochable inventory.
Actually, there is a cost: you have to pay to send books to other users.
Since BookMooch uses points as currency, your trades do not have to be direct swaps with other users, as they do on the free trading site, SwapTree. On the other hand, on SwapTree you can trade more than just books.
BookMooch also has a browser bookmarklet, the MoochBar, that will find books on the Web page you're on and add them to your want list or to your inventory. So if you're on Amazon and see a book you want, you can easily Mooch it. You'll have to wait for a BookMooch user to send it, but it will obviously cost you a lot less than buying it new.
BookMooch is run by John Buckman, who told me that when it comes to making money from the site, "I totally don't care." He made a lifetime of earnings selling his e-mail company, Lyris. Good for him. While there are too many swapping networks right now, the financial model of this one is in line with the negligible cash value of most used books.