According to About.com, cats stare from a distance without blinking when they wish to show control, dominance or aggression. Staring with eyes that are partially open can indicate fear or aggression.
According to the Humane Society of the United States, the meaning of a cat's stare depends on the state of the pupils. Staring with pupils constricted can indicate aggression or sometimes content. Staring with large, dilated pupils often indicates that a cat feels nervous or submissive. Cats who stare with large, dilated eyes are sometimes in playful moods.
The Humane Society also points out that cats use their body, tail and ears in addition to their eyes to communicate emotions. In order to accurately read a cat's emotions, it is important to examine all four of these elements. Forward, alert ears, for example, indicate a happy cat, while backwards ears indicate anger or fright. A tail that is erect with flat fur indicates happiness, while a tail held straight up indicates excitement. Cats that arch their backs are acting aggressive and angry, while cats that lie on their backs and purr while staring at you are very relaxed. If a cat growls while lying on its back, it is upset and ready to attack.