Each Yubikey would be unique. Your web application would associate the public ID of each yubikey (the first 12 characters of the OTP string) to the users account and then submit the entire string to the YubiCloud to know if it is valid. There would be no reason to reprogram the individual YubiKeys in this instance.
Check out the Development Guidelines (
http://www.yubico.com/development-guidelines) documentation (as well as the existing API/auth modules) for direction on how this gets implimented in your web app.