I won't get into too much detail about the Invasion, Although if you want to, go to http://en.wikipedia.org/wiki/Operation_Barbarossa .
The question comes: What if it had not happened, what then would have been the fate of the world ?
Completely different, would be two words to sum it up. Here is a map of the power of the Third Reich of Nazi Germany.
Suppose Hitler and the USSR had a longer truce, say lasting till 1945. Hitler would have probably been planning for an invasion of the British Isles. Actually, it is true that Hitler DID actually plan an invasion of the British Isles but decided not to in order to invade the USSR.
Hitler could also have convinced General Franco (Leader of Spain) to join them, which he would probably do.
In the early 1940s, the Axis powers were crushing the British in North Africa, specifically Egypt. At some point in this stage, the US would have joined the war and send their soldiers and equipment to help the British. At some stage, probably 1943, the Germans and the Italians would have overrun the Allies in Egypt and Captured the Suez Canal thus separating Britain, the protectorates of Gibraltar and Malta, from the rest of the British Empire who are forced to sail around Africa towards India for supplies. With the lack of supply, the Axis would've quickly overrun the Garrisons of Both protectorates.
Turkey, now just blocking the Axis from invading the Middle East, is being tempted to join both sides, If Turkey were to join the Axis, it would surely be on a promise that the '' Ottoman'' Empire would be rebuilt and that Turkey would occupy most of the Middle East, in exchange for Turkish Allegiance. If Turkey were to join the the Allies, Turkey would surely lose, as they would probably delay the Axis Offensive in the Middle East from 4 months to up to 2 years with Allied Help and could even launch an offensive into Bulgaria, establishing a Bulwark of the Middle East.
I'll continue with the Idea that Turkey joined the Axis, And would invade Syria, Northern Iraq and Lebanon. Saudi Arabia might make a non-aggression pact with the Axis to avoid a conflict. Persia, who at the time was a pro-Axis supporter would probably have joined the Axis and launched a major offensive into Southern Iraq.
Now, the Middle East has been wiped out, Mainland Britain is under attack, America, desperately, sends its soldiers to their deaths in an effort to save Freedom & Democracy. With that said, The British would probably sign an armistice, seceding all of her colonies to the Axis and with the British having to their own independence, at the cost of paying reparations. Soon after, Allied countries will follow in suit.
And to think, this all could have happened if Hitler had just decided to change his mind.
Note: These are all the things that I thought would have happened and in no way do I say that it ' will ' happen, I merely am giving an example of what COULD have happened.