Cat people have interpreted the consuming cat stare as its way of telling that it's hungry, angry or anxious. Others believe it's the cat's way to size up anyone and anything as determined by one rule: the one who blinks first loses. If you engage a cat in a staring contest, the odds will never be in your favor, unless you cheat.
People find staring rude, but not cats. Cats love to stare. Some cat experts believe cats stare at humans because they find them highly interesting. In fact, it could even be an expression of affection, especially when the cat breaks its stare to head-butt a person's face.
But from one cat to another, the stares could make or break a war. Dominant cats talk and stalk with their eyes. A slit-eyed cat intently watching another cat or animal indicates its readiness to fight if provoked, and the wide-eyed cat that notices this should turn tail and scat.
Next time a cat stares at you, don't just stare back but also listen and look for other visual clues to help you understand its mood. I've noticed that my cats' stares are usually accompanied by a soft rumbling purr or a light flexing out of claws as if they want to knead. If you are patient, the cat could later reward you with a light pawing or strong head-butting of your face. Whether you blink or not, either way you win. – AJB