The drivers had to be creative and careful, as many parts of the world still did not have paved roads – or roads at all. At times, the contestants elected to drive on railroads for hundreds of miles at a time. Often, their daily progress was measured in feet, not miles.
When a few of the teams reached Alaska, terrible conditions made the roads impassable. The course was rerouted to Seattle, where teams shipped across the Pacific Ocean to Japan. Only three of the drivers made it to Russia, where the race was exceedingly difficult, given that the drivers were passing through the tundra during the spring thaw and there were very few actual roads in existence.
The American car, the Thomas Flyer, eventually arrived in Paris on July 30, 1908. Although this was four days after the Germans arrived, the Americans were given the victory because the German team was penalized for not going to Alaska and shipping their car part of the way by rail.
The Italian team arrived in Paris in September 1908.
The race had far-reaching effects, as it demonstrated how the automobile had become a more reliable means of transportation, thus playing a role in the car's acceptance into daily life. The race also strengthened the call for improving road infrastructure.
George Schuster, the American driver, was inducted into the Automobile Hall of Fame in 2010.
For more info on the race, see this excellent write up from the Smithsonian.