Join the Fan Club
Every natural gas appliance produces exhaust. Most of the time, most of the exhaust is regular air + carbon dioxide (CO2) + water vapor . But there can be carbon monoxide (CO), and even a little bit can cause problems if it starts to collect inside the house.
Because of all of that (you don't want lots of extra CO2 or water vapor, though they don't have the same dangers as CO), every natural gas appliance is vented to the outdoors. For a furnace or water heater, that is typically a vent that is attached to the appliance. For a cooktop that wouldn't work very well, so the normal solution is a fan above the cooktop. A nice side effect is that the fan will help remove cooking smells. But even if you are just boiling water, turn on the exhaust fan. A cooktop exhaust fan won't take care of all CO2 and CO, but it will help significantly, both removing the problem gases and drawing in fresh air.
Carbon Monoxide Detectors
We are all familiar with smoke detectors. Everyone should have them because there are many different sources of fire (smoking, electrical, combustion appliances, etc.) But anyone with any combustion appliances (natural gas, propane or fuel oil) should have carbon monoxide detectors.
Ideal is to have one near (but not too close, to avoid nuisance alarms) each combustion appliance, as well as at least one in or near the bedrooms. Even though the detectors near the appliances should react first (e.g., if your furnace has a problem in the middle of the night), at least one in the bedroom area is critical because the biggest risk is when people are asleep. But even when awake, the symptoms of CO poisoning are subtle enough (you won't smell anything like you might with a fire, and you won't smell mercaptan (the "natural gas smell") because it isn't a gas leak, it is incomplete combustion) that detectors can be truly life-saving.