When you don't change your cars air filter the engine cannot breathe properly so the engine could lose power, use more fuel and your engine will also run rich as it cannot get the proper amount of air coming into the combustion chambers.
So your engine will not be able to burn the fuel properly when the air filter is really clogged.
A cars air filter should be changed yearly or every 12,000 to 15,000 miles depending on how many miles you drive per year and how dirty the conditions you drive in are.
If you drive in more dusty conditions then you may need to change the air filter every 3,000 miles or so but if not then yearly or every 12,000 to 15,000 miles is good enough to change the air filter.
If you notice a decrease in fuel mileage or loss of engine performance then check the air filter and if the air filter has not been changed in a year or more then it's likely time to change the air filter.
Air filters are pretty cheap and I change my air filters every year regardless of mileage just as preventative maintenance.