The short answer is yes, with the air conditioning running the car burns more gas than without it. When the compressor runs, more engine power is in use, and therefore more gas is burned in the process.
The main argument against running the air conditioner, however, is whether it burns more gas than rolling down the windows. With the windows down, a car becomes less aerodynamic. The air that shoots in through the windows creates additional resistance or drag. Increased resistance means the car has to work harder to maintain its speed. Even the experts' opinions vary widely, from 45 to 75 miles per hour, as to what speed makes the drag greater than the effect of the air conditioner.
