Which invention had the greatest impact on American transportation?
The train and the airplane were amazing in their own right--you could cross the continent quickly and safely--but most Americans spent their entire lives within a few miles of where they were born until the 1920s, when automobile ownership became commonplace. Moving to another town or state, or commuting to work in a different city from where you lived, was physically possible in a way it hadn't been before then.
People had dreamed of going to the city for a new life, of reinventing themselves away from the reputations they had acquired and the failures they had endured, or pursuing a dream of going out west, but lacked the means to do so. Owning a car was suddenly within the means of most working Americans and it gave them options they had never had.
There were Canals and Steamboats, but I personally think Railroads had to most impact. One advantage they had over canals, were that they were cheaper to build and did not freeze over during winter.
It helped connect the Western farming economy to the Eastern manufacturing areas.