Also note that delivery service is not available to the Swan and Dolphin, or to the Downtown Disney hotels, only to the Disney-owned hotels on site.
For those not staying at a Disney hotel, another option is available: your packages can be delivered to the front of the park, where you can pick them up on the way out. This usually takes a few hours, so you can't use it near the end of the day, but it is also free, and allows you to buy stuff without having to drage it around the park the rest of the day.