Wow, so far we've gotten some really good answers, and some really good historical discussion.
My aim in starting this post was to show that some things in History that are taken as simple fact are often very debatable. So far this thread has more than shown that.
I think Boroda has a very good point, that perceptions of history are incredibly important to understand. I think its true that the Western perspective on the USSR has been slanted by some fearmongering, and that manypeople in the West who lived through the Cold War do not have an accurate picture of that country during the same period. Many Americans think the USSR was like Col. Spicket from Tailspin (was that his name?). Americans forget that MANY Russians, East Germans and others in the Communist block were happy with their situation. Many East Germans are still upset at issues they consider unresolved from unification.
Filth's answer of 1918 is also a very good one. Personally I believe the two wars are better understood as one long conflict period, and in this sense 1918, with the coming of the Russian Revolution and eventual victory of the Bolsheviks, can be considered a good beginning of animosities. Still, the USSR was not powerful enough to prove a real threat to the West till well into the second War. Some of the dates being suggested after the war are arguably valid as well.
I still stick by my Yalta conference answer, which was Feb 1945. Any other answers out there?