One reaction that I always have when I read this story is how conveniently Ray Bradbury sidesteps the time paradox issue.  The paradox that I'm talking about is the paradox present in the Back to the Future movies.  In those movies, it was a big problem if you went back in time and met yourself.  In "A Sound of Thunder," Bradbury sidesteps the entire problem by simply saying that kind of thing isn't possible. 

"That'd be a paradox," said the latter. "Time doesn't permit that sort of mess­ -- a man meeting  himself. When such   occasions threaten, Time steps aside. Like an airplane hitting an air pocket.

I always find it interesting how Bradbury so quickly deals with one of the all time great time travel questions.  "What if you could meet yourself?"  Bradbury cuts the possibility out in a few sentences and provides no further explanation.  

Another reaction of mine is always regarding the consequences of Eckels's actions.  I've always known that making small changes within a system can create large changes later, but Bradbury's story takes it beyond anything my imagination would come up with.  The death of a single butterfly having the power to change a country's entire political alignment millions of years later is an incredible illustration of "The Butterfly Effect."