Fear of course plays a vital role in this great short story, both in terms of the fear that the narrator inspires in the old man whom he kills, and in the way in which the old man's eye inspires fear in the mind of the narrator.
One of the disturbing aspects of this story is the way that the narrator knowingly rejoices in the fear that he is causing in the old man as he creeps towards his bed to kill him. Note how this is described in the text:
Presently I heard a slight groan, and I kenw it was the groan of mortal terror. It was not a groan of pain or of grief--oh, no!--it was the low stilfed sound that arises from the bottom of the soul when overcharged with awe... I say I knew it well. I knew what the old man felt, and pitied him, although I chuckled at heart.
The reader is appalled by the way in which the narrator finds amusement in the mortal terror he is causing the old man to feel. However, at the same time, this is not a one-way process. As the narrator opens his lantern to reveal a crevice of light, it chances to fall upon the old man's eye. Note the response of the narrator to this sight:
It was open--wide, wide, open--and I grew furious as I gazed upon it. I saw it with perfect distinctness--all a dull blue, with a hideous veil over it that chilled the very marrow in my bones; but I could see nothign else of the old man's face or person: for I had directed the ray as if by instinct, precisely upon the damned spot.
Thus we can see that it is in part the terror and state of fear that the old man's "vulture eye" inspires in the narrator that causes the narrator to seek to end the old man's life. Thus we can argue that fear, as experienced by both characters, is the "natural state of being" in this story.