The Online Family answers:

Travel web sites such as Travelocity, Expedia or American Express may require up-front payment for a hotel stay, but it depends on the hotel’s requirements. For example, this is a common stipulation when booking a hotel stay in a popular tourist destination like New York during high season. Pay attention to the cancellation cutoff date when making a booking online. For instance, Travelocity’s FAQ says, “Any changes may be subject to a cancellation fee plus any applicable penalties if your cancellation or change request is made after the cutoff date.” As you’ve noticed, sometimes the cutoff date is the day you make the reservation and pay for the full stay. Though you can save money booking through online travel sites, if it’s flexibility you want, you might try contacting the hotel directly for a reservation to see if they require prepayment.