It's fitting that the first lines of Atlas Shrugged are ones of fear, given that the novel depicts a dystopian world and an impending apocalyptic collapse of society. Things like that do tend to inspire a little fear. What people fear in the novel (perhaps even more than what they love) tells us a lot about their characters and the book's overall philosophy.
There are two opposite fears here: the fear of change and the fear of standing still. While James begs for stability and panics at the idea of uncontrolled change, Dagny panics when her train stops moving, and is horrified to see the world grinding to a halt. Both fears are actually two sides of the same coin; they each see world destruction as the end result of their respective fears.
Fear is a universal constant in a world going to pieces, but it is also a character barometer. People in this book are defined by how they handle fear, how they define fear, and how they conquer fear or let it consume them.
James Taggart is the character most defined by fear in the book, although his fears are the least well defined.
Eddie is the character through whom we experience fear most clearly.