When I saw the title of the thread, I asked to myself "which one?".
In reality, the WW II was a "continuation", or if you like a somehow necessary consequence of how the things were settled (or not) in the first one.
This thread somehow attracted me for some time, but it was not until I read this article in Asia Times that I decided to participate:
http://www.atimes.com/atimes/China/ML15Ad01.html
The article by an Italian "expert about China", deals with paralelism between the trayectory of Germany in the XX Century and that of China in the lasts and coming years...
as scientific, economical and military powers that by its mere existance, "subvert" the established "status quo".
(By the way, it includes a comment or two about the issue of "German arrogance", that I think were mentioned recently on the forum)
By the way, it is my opportunity to recomend to "Muzungu" and "Cimerianbroke" this book:
http://www.amazon.de/Aufstieg-Untergang-Republik-Weimar-1918-1933/dp/3548265081
On the other hand, I don't know if in Germany the subject is popular, but at least in the literature in English, every so often appear these fictions novels about the posibility of a Germany victory in WWII, some of them even taken to the screen...
http://en.wikipedia.org/wiki/Fatherland_(novel)
Now, answering the direct question posed by @edao... (in the understanding that my answers reflect my personal values)
Would Europe be a better place to live if Germany had won the war?
No.
Certainly not for Jews, Gipsis and a lot of minorities, religious, racial and of sexual preferences.
These would have been exterminated altogether.
Then the Slavs would have been enslaved and subject to slow genocide (almost all Eastern Europe).
Even the "Mischlinge" from South Europeans were undesired (e.g. with Italians and Greeks).
Europe could have been "better", but only to Germans.
Would a united Europe run by Germany have stopped America dominating the world in the way it has over the last 50 years?
I don't know.
What role would a German Empire have played in the cold war?
There would have been no cold war, at least not against the USSR/Russia... but probably one between the USA and Europe.
Anyway, for that to happen once the war actually happen, the Germans must have defeated the USA and/or the Russians, which actually would have been very difficult.
As an example, lets remember that the Russians sustained arround 7-8 million casualties in 1941 alone. And they were able to stop the Wehrmacht and become a more efficient and large war machine every succesive year of the war.
The Americans had more industry than Germany, and at the end, the vision to have A-bombs by 1945.
Victory of Germany after 1942: Impossible.
Would we be speaking German and would that be a bad thing?
German is a beautiful language (once you more or less understand its complexities).
I don't think that the only reasons that English is so widespread is only because of colonialism, trade, and the popularity of the Angloamerican culture.
English is a very simple an easy language to learn.
Even other Europeans, do not make the effort learn much German.
Maybe some of us will have some confirmation about it in the case of future internationalitation (or not) of Chinese.
Looking at the current crisis Germany seems by far to be the best run country in Europe, they now seem to be dictating terms of economic management to half of Europe via the back door. Germany are now turning away from Nuclear power and have an economy based more on manufacturing real things instead of playing with number in financial casinos.
Germany has been doing better than most other countries in Europe. One or two years ago, in a theme about Turkey, I said that Germany (and Turkey) will survive better an economic crisis than some other countries that dedicated themselves to not very productive things, including some in the South dedicated, whose finances weren mostly about money laundering.
Even when I do not hold for impossible that Germany too could show signs of weakness in the following years (they are Germans, not Martians), I admit that they are showing themseves as the great economical and historical force that was begining to be evident at the begining of the XX Century, and it seems that its rise as conductor of Europe, was finally irrepresible.
Regards.