Every driver handles their oil system differently. Some like to do everything themselves, while others use quick lube shops so they don't have to worry about it. There's also differing philosophies on when exactly one should add oil - should the system be topped off regularly, or only when it absolutely needs it?
Most cars today hold four quarts of oil. However, the engine needs to use nearly all of that oil to function at peak efficiency. Oil will naturally decrease over time, which is what necessitates oil changes and adding more every now and again. While systems like the wiper fluid can pretty much function until it's completely gone, there needs to be a certain level of oil in the car to ensure things run safely.
The dipstick in your engine will be able to tell you how much oil is in your car. Remove the dipstick and wipe it down clean with a rag, then reinsert it. The oil should come up to certain marks on the dipstick. Common phrases that drivers will see are "low" and "add."
The difference between these two markers is important. When the oil only reaches up to or below "add" level, it's time to immediately top up the system. The question then arises whether a driver needs to add oil when it's merely "low" or above that point.
Essentially, there should be no problem running the vehicle under normal conditions when it reads "low." However, there can be a danger in extreme situations. Oil acts as a heat sink for the vehicle, and the more oil there is the better the car can handle hot temperatures. The oil isn't the only aspect that helps cool the car - that's mainly the radiator's job. But it does transfer heat from some key bearings.
So if you're planning on driving in very hot weather, going on a long road trip, towing a trailer or doing anything else that would put undue strain on your engine, it's a smart idea to top up your oil. Even if it hasn't reached the "add" level yet, this will ensure that the engine doesn't sustain damage during this activity. Be careful not to overfill the engine, however, as this can cause other problems.
It's also a good idea to keep a few cases of motor oil in your vehicle in case of an emergency.