Eye contact can also be a way of establishing dominance. If you often avert your gaze your cat may assume that she is the dominant party in the relationship! For this reason, many cats can find sustained direct eye contact to be aggressive. If you do not know a cat well, do not stare at her too much or you could make her nervous. Other cats, and cats who know you well seem to love your attention and will meow repetitively until you look at them!
However, taking a cat on at a staring match can be rather time consuming and (depending on your relationship with the cat in question) could end in tears. Some cats (particularly young males) can get a "mad look" in their eyes which will be followed by an attack run. Their eyes will be very wide and their pupils large and, while the intent is probably not to actually hunt you, they may also wiggle their back legs in preparation for launching an attack. If your cat does this, it is probably best not to stare back unless you are ready for a wrestle.
Seti, in his younger wilder days, would regularly hide in our hallway and launch very effective ambushes on unsuspecting humans. He would also get the "mad look" just before charging out with his paws raised to box with us - thankfully he is was just playing and never did any real damage!
Loki on the other hand, simply loves to be watched by humans and conducts all of his stalking and hunting practice against poor Seti. Loki will happily take you on in a staring contest without ever becoming aggressive - just don't expect to beat him as he can apparently stare four hours without needing to blink.
Some cats will blink or wink as a greeting. When cats blink at each other, they are indicating that they are not threatened or threatening and so can be a sign of great affection between cats. If you blink or wink at your cat in an exaggerated manner, she may blink back!
If a cat feels defensive, she may dilate her pupils in order to increase the width of her peripheral vision so that she may successfully counter any attack. Just before an attacking cat pounces she may narrow her eyes in order to focus exclusively on her target and to maximise her depth perception.