Nietzche has said, "Even great spirits have only their five fingers breadth of experience - just beyond it their thinking ceases and their endless empty space and stupidity begins." If there's one thing that is common among every human on this earth, it's that none of us have experienced death. You could mention the subjects of medical resuscitation as exceptions, but I have yet to hear of someone fitting that description who could give a clear answer when asked, "what was it like?" Furthermore, if there's one fear common among all people, it's the fear of the unknown. With all of this taken into consideration it makes nothing but complete sense that people would be naturally afraid of dying.
The amygdala is a part of the brain that governs emotions related to self-preservation. Without it, there would be a severe numbing of temperament, leading to a lack of motivation, and an apathy toward living. This is something we share with every organism in existence. Everything from killer whales to dandelions have a concept of self-preservation. Death is universally undesirable.
So what about the people who aren't afraid. Are their thoughts unnatural? Hardly.
The most common reason for this phenomenon is the presence of spiritual belief regarding some sort of afterlife. Christianity teaches of a heaven for those who are saved in Jesus Christ and Hell for those who aren't. Some religions including buddhism and hinduism believe in the concept of reincarnation, or returning to earth in a different form after death. Something all of these ideas share is a message of hope. They dispel the fear that shrouds death in menacing darkness because death is no longer unknown. Faith makes them certain that this life isn't the end.
This is not to say that only people of some religion haven't fear. I would suppose for the others, how they feel about life develops their feelings on death. What I mean by that is, imagine someone who knows they're about to die is thinking back on their life experiences and decides that they've lived just the way they should have. This person would be more likely to welcome death as an eternal rest than someone in the same situation who has many regrets and isn't ready to leave.