Today, I ordered two different products from amazon. They were both priced roughly the same, and are both roughly the same size and weight. However, for one I elected to pay for standard shipping, and for the other I chose free shipping. The reason I did this was to compare how drastic the difference is. The last thing I ordered using free shipping took about three weeks to show up at my house.
Unsurprisingly, I received a notice from amazon that my order with paid shipping shipped today (same day as I placed the order). The estimated delivery date from UPS is Wednesday. I will not at all be surprised if I actually get that order before they even pull the other item off the shelf, and notify USPS that they will be shipping it.
Update (17-June-2009): Amazon Shipping, Part II