What if... Captain cook hadn't declared Australia terra nullius.
The British Empire would have taken it over saying that it's the white man's burden (or something like that) to teach the Aboriginals British sense, culture, and beliefs. The only thing I can see that would be of great change would be the chance that Australia would've been taken by another power or several powers.
You guys should read "Guns, Germs and Steel". It's a great book on why the world developed as it did and why certain powers on countries quickly built civilizations and industry while in other continents they're still running about with stone spears, or having a society that can't use the written word etc. Really interesting for speculation purposes.
What if Ögedei hadn't died when he did, and Subutai continued his conquest through Europe? Would we all be speaking Mongolian now? Doubtless to say the world would be a very different place.
The strength of the Mongolians were there horse archers and terror tactics. Now while horse archers are pretty much hell to other troops, they have a weakness: they're only really suitable on steppes or plains. Surely the Mongolian forces could charge through Hungary and perhaps even reach Central Europe, but there they would face different terrain. Mountains that cannot be easily traversed by horses. Now yes, of course it could be traveled by horse, but it's risky, which is why mountain cultures don't rely on horses that much.
With their main advantage becoming a disadvantage, the armies wouldn't be able to breach Germany, Italy, and the rest of Europe. They might have been able to sail to Italy and other parts of the region, but it's doubtful they would be able to hold their conquests.
Technology would surely be impacted; the Mongolians allowed cultures to mingle and trade new ideas with each other. Surely certain parts of Europe would have benefited.
It is also probable that a large number of Mongolians would have decided to stay in Europe...Which would be hard for me to discuss in-depth.
In short, the Mongolian forces would eventually be stopped by the terrain.
What if...
The Roman Empire ( Augustus Caesar's reign ) expanded even more than it did historically?
The stability of the empire would be called into question.
Expanding into the east would be suicidal; Persia (under the Parthians I think) were an empire in their own right and was a hard opponent, all through out history. I would believe that the Romans would be forced to sign a peace treaty eventually, although I doubt much would come of it.
Expanding into the north would be somewhat easier...It would take ages to subjugate the rest of Germany and the British Isles and even more for Scandinavia. If somehow they were all conquered, it would be difficult to rule. The organisation, the military spending...The supplying of the legions and officials...
Expanding south would be...useless. All the good land is miles and miles south, way too far out of reach.
In short, expansion would hurt and probably be reversed in a few years time.
I'm done. My answers might not make sense, but I wasn't really trying to be articulate.
My turn...
What if...
The crusaders of the 4th Crusade had had enough funding to pay Venice for their ships and not had to go and pillage Constantinople?