Yes, olive oil does go bad after a period of time that is influenced heavily by the conditions in which the oil is stored. Once olives are picked, they slowly start decay just like any other food, and the nutrients and enzymes that make olive oil famous for its healthful properties begin to break down and turn rancid.
The best time to consume olive oil is within the first six months after production, as it will have the most flavor and antioxidant retention during that time. After about a year, the oil will not have the same taste as before, though some people are more sensitive to the degradation than others. The oil will not make you sick, but it will not be as good for you as when it was fresh.
Olive oil bottles are supposed to have manufacturing dates and expiration dates printed right on the label, however, often times these stamps are mysteriously missing. Usually, the expiration dates specified by the manufacturer range from about 1 to 2 years after the date of production, but if you are consuming olive oil for health reasons, I would suggest that you replace an old bottle before one year is up.
Heat and light affect the rate of olive oil degradation
One variable that heavily influences the length of time it takes for olive oil to go bad are the conditions that the container is stored in. Olive oil is highly sensitive to light and heat, and will chemically break down much faster when exposed to sunlight or temperatures greater than room temperature.
For this reason, never buy olive oil that is stored in clear containers, either glass or plastic, because sunlight and incandescent light can both cause olive oil to go bad more quickly. Always opt for opaque colored bottles, which is usually an indication of the higher grade oil as well.
Olive oil may be stored at room temperature, but will last much longer if you keep in the refrigerator. Some olive oil labels recommend that you do not store it in the refrigerator because it will make the product cloudy, but it will not damage the oil and will in fact prolong shelf life. And when the oil is brought back to room temperature the cloudiness goes away.
As a personal preference, I have actually have gotten used to the taste of refrigerated olive oil and I think it tastes best that way. In any case, for best results at least store it in a cabinet or pantry where it is protected from light.
When olive oil starts to go bad you will be able to taste it, however, some people are more sensitive to the subtle changes in taste than others. Older and even bad/rancid olive oil will not hurt you, in fact many people around the world consume rancid olive oil due to the unavailability of adequate refrigeration and storage.
Just keep in mind that one of the main reasons for adding olive oil to your diet is to get the healthy antioxidants and enzymes available in fresh olive oil. If you let your olive oil get old you are defeating the purpose, and it is a worthwhile to invest in a new bottle and discard the old.