Though there is no scientific proof that cats have a sixth sense, there is plenty of anecdotal evidence which shows how cats behave differently when their owner is sick, sad or pregnant.
There are many stories about cancer patients and their cats. When cancer patients are going through chemotherapy and radiation, they are often surprised to see their cats spending day and night with them by their side which they have never done before. By the time the patients get better, their cats swiftly return to their old routines.
Another example is about pregnant women. It is interesting to see how cats can sense a woman being pregnant. Some may react by jumping on the preggo woman's belly, lying comfortably on it to feel the warmth and slight vibration. There have been many responses from pregnant women that their cats' behavior changes from being indifferent to more loving and protective or in some cases aggressive.
Cats are very sensitive to small changes their cat owners make. They can detect differences in your mood, behavior, body chemistry, posture and so forth. All these little clues help them understand what you may be going through. Cats are really good at reading body language as they communicate with their peers by giving each other physical signals.
When a woman is pregnant or when someone falls sick, their body chemistry varies accordingly which cause the person to emit a slight different scent that can be easily detected by cats. In fact, cats can tell if their peers are sick by the way they smell.
CBS News.com covered a story about a cat that can predict death, but now we know why the cat seems to be able to foretell what's coming.