I paid for Overnight Delivery from Fedex when I shipped an order from Amazon.com. I ordered my package on Saturday and knew it wasn't going to get shipped out until Monday, with a Tuesday Delivery.
Fedex didn't even pick up my package until late Monday night, and even though they only had to move it from Nevada to California, they somehow managed to take until Friday to deliver my "overnight" package, with the package sitting in a shipping facility in California for two days.
While this package wasn't particularly time sensitive, I did pay for overnight service and was looking forward to my package on Tuesday. This is why I always use UPS.