World War II was a conflict on Earth from 1939-1945, considered the most destructive conflict in Earth's recorded history. It opposed the Allies (mainly the United States of America, United Kingdom, Soviet Union, France and China) against the Axis (Germany, Italy, Japan). Although the war was begun by the Axis (Germany, Japan, Italy and a few "satellite states"), it would eventually be won by the Allies.
World War II marked the first experiments with the Stargate; fearing that it was a weapon, the American government had it transferred from Giza to the United States to keep it out of the hands of the Nazis, who were on the brink of invading Egypt. Franklin D. Roosevelt, who was "curious" about it's potential, authorized experimentation to learn what it was capable of. Professor Paul Langford and Ernest Littlefield led experiments in it, but it was abandoned after Littlefield was presumed killed after stepping through the Gate. (SG1: "The Torment of Tantalus")
After the War's end, the Soviet Union, which had played a major role in defeating Germany, scavenged the DHD to the Alpha Gate found by Langford in Giza from somewhere in its occupation zone. (SG1: "Watergate")
The former allies didn't stay together for long. Instead, the ideological conflicts prevalent long before the war surfaced once again, and the "Cold War" began.