One day several summers ago, we were called out to a family's home to take a look at why their air conditioning was not cooling their home, and what was causing their energy use to be much higher than normal. Upon entering their home we noticed that they had a ceiling fan in every room and they were all running at the same time. Next, their air conditioning system was checked and it was verified that the operation of it was correct. We asked if their A/C system always worked poorly, when the temperature got to the upper nineties, and they said "no" it had just been recently. We asked them if they always had ceiling fans in every room, and they said "no" (only one in the kitchen). They said they had read that ceiling fans would save them money on their cooling bills, so they had them installed.
Almost everyone has heard that ceiling fans will save money on cooling bills. When the air around us is moving, we usually feel cooler. This is because moving air evaporates our sweat faster than still air. Evaporating sweat cools us down faster than anything else, even slightly cooler air temperatures.
However, running a ceiling fan actually causes an air conditioned room to heat back up faster. The surfaces of the ceiling, exterior walls, and windows are warmer than the rest of the room. When you turn on a ceiling fan, it circulates the air in the room. This mixes the air in the room faster, which makes the air cooler next to the walls and ceiling, which in turn makes heat move faster through the walls into the room from outside. Ceiling fans only cool people down, not rooms, so if the fan is on and no one is in the room you are wasting electricity.
If your A/C is always on, then using ceiling fans will save you money if you use them only when you are in the room, and set your house thermostat to a slightly higher temperature. If you forget and leave them on when you leave the room, you won't save money. Running ceiling fans will cost you more money because your A/C unit will have to do more cooling, and the electricity burned by the fan will be completely wasted.
The reason that this family's energy use was so much higher, was that they had fans installed in every room of their home, and they had every one of them on continuously. Heat from outside was transferred into their home much faster, and it was so much faster that the A/C system couldn't even keep up. There was nothing at all the matter with the air conditioning system - the ceiling fans caused the higher energy use.