I agree, cats have a peculiar sense of taste. My cat will drink water from a dirty cup of coffee in the sink, but will ignore the totally clean bowl of water that I leave out for him (and change at least twice a day).

Theoretically, cats drink only fresh, preferably running water (unlike dogs who will  drink just about anything). If water has been standing for a while then cats treat it as "not fresh", and ignore it. However modern cats who live in modern homes have come into contact with a variety of different tastes and smells, and have therefore developed some very peverse drinking habits.