You may have wondered why television pledge drives offer CDs, books, artwork and event tickets in exchange for your charitable pledge. They're not just trying to entice you. When a charity offers something in return for your donation, your pledge becomes a legal agreement in the eyes of the law. Your generosity creates obligation on your part and on the part of the charity.
If you agree to make a donation and a charity agrees to provide "consideration" in return, you have a legally binding contract. "Consideration" can be a promise to send you a gift or a promise to take some action, such as mounting a plaque with your name on it. A verbal agreement counts as a contract, so a phone call during a telethon can be binding, especially if you called in response to the offer of a gift in exchange for your donation.
If your "gift" does not arrive from the charity, you could successfully claim that the contract you entered is no longer in effect. At that point, you could justify cancelling your payment to the charity. In practice, once you notify the charity that you didn't receive the gift, the charity can simply send it and claim it has fulfilled the contract.
If you receive consideration and decide to back out on your pledge, you don't have much legal ground to stand on. If the charity insists on your payment, it will probably find the courts will favor its stance. A charity isn't likely to go after you for a $10 donation, but it could find it worthwhile if the amount is large enough to justify legal expenses.
Most small pledges occur with credit cards. Once you permit the charity to charge your credit card, you have indicated that you agreed to the contract. However, if you have a problem, such as not receiving consideration, you can dispute the charge on your card. Your credit card company will investigate the matter, and it could return your money if you successfully show that the charity did not do what it said it would do in exchange for your donation.