Yes, using the air conditioning in a vehicle will use slightly more fuel as the air conditioning compressor gets its power from the engine of the vehicle, and so more fuel will be needed to make it function.
However, due to the significantly increased efficiency of air conditioning systems, on a modern car, having the window open will often increase fuel consumption by more than running the Air Conditioning systems.
Also, not using your air-conditioning can increase costs. Without oil being fed around the system to lubricant the components, the system can dry out, damaging the compressor and causing hoses and connectors to leak.
It is, therefore, advised that you run your air-con at least once per week for a while whilst driving to prevent any unnecessary damage to the system.