Aside from thwacking it with an axe or baseball bat, it's not that easy to outright break, with intent, your central air conditioning system. But it is possible, over the long run, to inflict serious damage on it while never laying a finger on it. Chronic owner negligence can wreak havoc on not just your AC, but your home and even your family.
Running your AC with a dirty filter will allow, over time, a buildup of dirt and dust on the evaporator coils, the blower and the compressor, which will lead to inefficiency and a possible breakdown. Also, everyone in your home will be inhaling the particles the filter should be catching. This can trigger allergies and breathing problems. Change the filter in your air conditioner every one or two months during peak use. Exactly how often depends on the kind of filter you buy, how much your AC runs and how dusty it gets in your home.
Dirty Outside Coil
It's easy for the outside condenser coil to get dirty, but unlike the evaporator coil inside your house, the outside coil is easy to inspect and clean. A dirty coil restricts airflow and lowers efficiency. Every year, inspect the outside coil and housing for dirt and debris. Make sure there's a couple feet of open space between the unit and nearby vegetation. Many newer AC units have tougher coil fins, which won't bend or break like the older aluminum ones. Either way, take care not to damage them when brushing off debris because bent fins diminish airflow.
Clogged Condensation Line
Ensure that your AC's condensation line is never clogged. Backed-up water can leak out of the AC coil box inside your home and ruin your walls or floor, or it could leak into the electronics of your AC system and force major repairs. One way to try to unclog the line is to connect a shop vac to the drain line outside your house and suck out any grime. Older homes may not have an outside drain line, so a clog might need a professional's help. Once a year, pour a diluted bleach solution in the PVC, indoor condensation line to kill clog-causing algae.
If you don't think your AC is cooling your house properly, and you've checked the inside and outside units, consider the ducts. Check for obvious obstructions in the attic or basement. Because your HVAC ducts are vast and sometimes hard to get to, it can be difficult to figure out exactly where the problem is and repair it properly. You might have to call in a professional.