According to About.com, if your air conditioner keeps blowing fuses or tripping circuit breakers, it is because the appliance is trying to draw more current than the fuse or breaker will allow. This can result from a window-mounted air conditioner being plugged into a circuit that is insufficient for its needs, or it could indicate that the air conditioner needs servicing.
Circuit breakers and fuses are rated for a certain number of amperes. If the current goes above the rated amperes for more than a few seconds, the mechanism breaks the circuit. This is to prevent the excess heating that overcurrent can cause in the wiring and ultimately prevents fires. If an air conditioner's circuit is simply not powerful enough for its needs, the fuse blows every time the unit is started.
When an air conditioner begins blowing fuses while connected to a properly rated circuit, it could indicate a problem with the compressor. If the compressor has difficulty starting up, it can increase the amount of amperes the unit attempts to draw, overpowering the circuit and blowing the fuse. In any case, blown fuses should not be ignored. The unit should be checked by a professional to prevent a possible electrical fire.