Why won't your cat drink water?

I'm not a cat expert, but I think that cats can sense whether or not their food and water may make them sick. Cats have a great sense of smell and water from different sources have different odors. Cats may also detect odors better than humans. Therefore, cats maybe sensitive to chemicals in water or water from an unfamiliar source.

ADD:

The first answer is quite right; cats have an extremely sensitive sense of smell, and can easily detect any decomposing proteins in their food or water, so will only often touch fresh, moving water. However, there is a little more to it than cats turning their noses up at water just because they don't like the smell:

Domestic cats, like their wild ancestors and cousins, are designed to get their moisture from their food, so will not often drink water out of a bowl or other water source unless very thirsty. Investing in a water fountain specially designed for cats is an Excellent way of enticing a cat to drink, as the water is constantly moving and kept fresh.