A clogged air filter in a air conditioner will lead to the evaporator freezing. A frozen evaporator will not allow any air to pass by it. This could cause serious damage to a compressor. As the suction line and evaporator freeze, there is a chance for freon, in the form of a liquid, to enter in to the compressor. As a rule of physics, you CAN NOT compress a liquid. This will damage the compressor permanently.

If you chose a filter that is more aggressive at removing particles from the air you breath, you have to check it and replace it more frequently as it will clog more frequently. I know what you are wondering  - how long should a filter last? The best person to answer that is you! How often to you dust your home and stir up dust? Do you have wood floors or carpet? Do you have a lot of traffic in your home? These are the top factors that will stir up dust. With the furnace running, the the filter is trapping this dust and other particles. The filter is slowly filling up. So checking the filter more often, rather than less often, never hurts.