Will the real Germany please stand?
An unsurprising yet always contentious and interesting topic for discussion. I don't know enough of the events surrounding the Great War to provide any sort of fresh insights, therefore I'll stick with the Second World War. And despite being a World War II buff (heck, aren't we all?), I'm not certain how fresh my insights might be in light of some of the quality posts so far. So here goes, nuthin'...
First and foremost, let us clarify what it means to "win the war". In the context of this discussion, it seems reasonable to propose this term means Germany has succeded in forcing either the conditional or unconditional surrender of Britian or the USSR or both; or some sort of geo-political/economic settlement favourable to Germany. If such terms are met then we may state Germany had won or could win the war.
Now, could Germany have won the war? There were certainly a number of factors in their favour: 1. Poland, Denmark, Norway, the Low Countries and France had fallen; thus, removing British allies from the continent. 2. The BEF was nearly destroyed in France and never truly recovered. 3. Britian did not have the manpower to sustain a protracted war (this became abundantly clear in the last stages of the war). 4. The Wermacht was the best trained, best led, and often though not always, the best equipped army in Europe, if not the entire world. The last of the great professional armies. 5. The Wermacht was supported by a highly skilled air force, namely the Luftwaffe. 6. The US, at least initially, was doing its best to remain out a lengthy European war. 7. Germany managed a political coup d' grace with the Molitov-Ribbentrop Pact. Not only did this agreement secure the destruction of an old German (and Russian) enemy, Poland, but it seemed to have lulled Stalin into a false sense of security in the East.
In the West, I think Germany had the potential to wear out the British, as long as the US or Soviet Union did not intervene (more about this later). Granted the Britsh Navy was formidable and would have done their best to prevent an amphibious invasion of the 'Home Islands'. Nonetheless, the British Army, for the most part, was poorly led and poorly trained in comparison to the Wermacht. Any time the two armies were on equal footing, the British were defeated. And whether or not the British public would have supported Churchill's admirable defiance in a protracted war without any other nation to share the casualties is debatable. Subsequently, Britian eventually suing for peace with Germany seems plausible.
In the East, I do believe Germany had the manpower and tactical ability to overrun European Russia and nearly did so twice. Barbarossa caught the Soviets on their heels and the Red Army was devastated by the initial thrust. Moscow was certainly within Germany's reach. Nonetheless, it is unclear whether the fall of Moscow would have led to the capitulation of the USSR. Incidentally, Stalin with his penchant for brutality and paranoia was not exactly the beloved leader of Mother Russia. If his government had collapsed, perhaps more Russians, especially ethnic Russians, would have fought alongside the Germans.
However, German failure, in my opinion, was not the result of economy, logistics, or manpower (though these are certainly significant factors) but largely the result of ideology. Germany's embrace of Nazi ideology doomed its people to inevitable defeat and doomed the people of Europe to a horrible fate. Nazism was a myopic, authoritarian, unimaginative, ethnocentric ideology that regarded war as the ultimate political tool. That is to say, amongst Nazis, war was not seen as sometimes necessary but unfortunate political outcome. Nazis desired war, they longed for it. Thus, Germany's military choices were always inextricably intertwinned with Nazi ideology.
It is true that if Germany had simply let the USSR alone until it had exhausted Britian, it could have concentrated its full military might on Russia. Yet this is an impossibility since Nazi ideology always viewed the conquest of Russia, along with the destruction of European Jews, as its primary goals.
Consequently, and thankfully, Nazi ideology inspired irrational decisions for Germany despite ample opportunity to chose rational, effective choices, e.g. murdering large pools of potential labour in conquered territories; starving inmates in labour camps while they perform useless tasks that only lead to death; military plans, such as the conquest of Stalingrad, based upon ideological rather than strategic goals; and so forth (I say "thankfully" not because I condone Germany's murderous rampage through Europe but "thankfully" because their ideology became their own undoing - at a horrible price, of course).
Therefore, I'd say Germany could not have won the war, at least in the sense described above, since Nazi ideology would never accept the most favourable circumstances to end the war, i.e. the partial conquest of the USSR was unacceptable.
Incidentally, the argument suggesting the Allies and the Soviet Union would have lost without US military and economic intervention is a 'Catch 22'. No one would argue the importance of American contributions on the battlefield and in the factories. Yet, neither the US or Britian had the stomach, if you will, to truly slug it out with Germany. The Germans approached the art of war with ruthless effeciency and outclassed the Allies on equal footing and often inflicted terrible casualties when outnumbered. The US and Britian were hestitant to commit their civilian armies to bloody campaigns. This, in part, explains the lacklustre and unimaginative leadership that often plagued Allied armies. Only Stalin had the cold-hearted determination and ruthlessness to make the "blood sacrifice" to ensure Germany's eventual defeat (and secure Soviet political ambitions). The outcome of the war appears unclear without the horrendous sacrifice of the Red Army.