I have to agree with DingBat. Part of the reason Germany lost the war was its lack of long term strategic thinking. Of course, it's not only that, but that certainly plays a large part of it.
1) As mentioned above, Germany (moreso Hitler) lacked the ability to iron out a long term strategic plan.
1a) Germany could have probably taken out England had it stuck to its guns and focused on English armament and military targets. Instead, to England's advantage, they changed their tactics to terror bombing cities.
i) As we all know, Germany quit focusing on England and turned its attention eastward.
ii) Realizing the superiority of the Spitfire very early on as well as finding out the hard way that it lacked the capabilities to escort its bomber fleet over English territory, Germany did little to solve these deficiencies.
iii) Germany had no long range heavy bomber throughout the war.
iv) If I'm not mistaken, Germany only had access to 87 octane (equivalent) fuel. This really limited Germany's internal combustion engine capabilities because the only way to improve the HP was to increase displacement, further increasing fuel consumption and weight. America and its allies had access to much higher octane fuel allowing for forced induction ala superchargers (higher octane = higher fuel stability at higher temperatures = you can pack more air into a cylinder ala forced induction without it detonating = more horsepower!).
v) Even if Germany had taken out England, it would have tied up a large chunk of the Wehrmacht simply occupying it, further decreasing its capabilities in waring in the east.
1b) Because of Hitler's lack of long term strategic planning as well as his dominating presense and distrust of the OKH, German Heer movements went about in ways that overextended its own capabilities. To paraphrase Erich von Manstein in his book
Lost Victories, no one ever thought that the assault on Russia might take two campaigns instead of one.
2) The German Wehrmacht was not a "modern" army as many are lead to believe. They were way ahead of their time in terms of leadership, training, morale, and tactical prowess, but as far as equipment is concerned, most of their adversaries were actually technologically superior to them. Its command structure was, in fact, very good, but Hitler's mingling with military matters and the OKH nullified this, as seen with the invasion of Normandy and no one wanting to awaken "der Fuhrer" from his morning slumber.
2a) We often forget that the German Army was a very young army. Rearmnament of Germany began in 1935, and it plunged itself into a world war just four years later. Logistics, supply, and mobility of troop movements, the real bread and butter of a military war machine, was largely horse cart driven. Germany did have a good rail system (largely destroyed by 1944), but rail can only go where rail lines are laid. Germany did not have the automotive industry like the United States did to equip the logistics side of its army. In Bidderman's memoirs of his accounts on the eastern front, he makes special mention of this. He goes on to say that whenever German units came across American made trucks, they made exceptional use out of them. Germans loved Ford trucks.
They were strong, reliable, and there were many spare parts available to fix them. Also, even if the Wehrmacht had been fully mechanized, Germany did not have the fuel supply to sustain it.
2b) I will refrain from going into much depth on this, as it's been mentioned time and time again in this thread, but Germany spent too much effort on side projects and "super weapons" that ultimately lead to nothing. By 1944, Germany didn't need improved tank designs. It simply needed more of them.
3) War in the east was inevitable. The idea of "labensraum" (sp?) was part of the core philosophy of Nazism, and Hitler made it very clear in his book
Mein Kampf of his intentions for Germany to expand eastward. Because this ties directly in with the Great Patriotic War, I must mention a few things here as well:
3a) Fascism and Communism are ideological opposites. Even if Hitler hadn't planned to expand eastward, Russia and Germany would have clashed eventually regardless.
3b) A lot of people forget that the might of the Red Army of 1944/45 only got that way because of its blood, sweat, tears, and losses of the previous years. As the war progressed, the Russians began learning and using Germany's tactics against them, and even more ironic was the fact that Germany began copying Russia's use of tactics that ultimately lead to their agonizing defeats of 41/42! Personal opinion here, if Russia would have attacked first, it would have been a rehash of its invasion of Germany during 1914 - a complete debacle. Morale is always on the side of those who gets attacked first.
4) America's developement of the Atom bomb was originally planned for Germany.
So, uhh, on to the real subject of this topic, what would have happened if Germany had "won" the war? Even if Germany had won the war in the east, it would have bleed itself dry in doing so. Losses for the Wehrmact in the first month of the campaign in Russia were higher than they had been in the first two previous years of war. By the end of 1941, Germany had sustained over a million casualties, and it was forced to rely much more heavily on its allies for manpower (Bulgaria, Romania, and Italy), whose fighting effectiveness are often put in question (this is not a knock against these three nations - Manstein goes into rational detail as to why this was in his book,
Lost Victories). Realistically, the war in Russia could have been won by 1943 had proper strategic planning been thought out prior to the invasion, but by this time, German losses would have been so high that its ability to reinforce a front against the United States would have been fairly limited. Not only that, Germany would have had to keep a large occupying force in Russia had the Soviets lost anyways. Even despite a homeland advantage, I don't see Germany holding its own against a sustained war against a nation with vastly superior industrial capabilities, population, and naval prowess like the United States. Remember, by winter 1944, the American army in Europe was larger than the Soviet's, and we were fighting on two fronts! Had Germany taken out England, however, the US would have never been able to invade Europe.
Then there is the internal power structure of the Nazi party...
All in all, even if Germany had "won" the war, it would have collapsed upon itself eventually. Over-extension of its territory, over-stretching its military capabilities, and lack of solid internal power structure would have eventually lead to its downfall, or worse, civil war.
(Sorry for the novel)
Sidenote - While the Sherman was an excellent tank in terms of mobility, ease of production, and reliability, its performance in Europe is the main reason the United States changed its armour doctrine after the war. Over half the German Panzers on the western front by the outset of the invasion of Normandy were Panthers, and while many were taken out by air, the American and British armour units just got downright mauled in tank vs tank combat. On another sidenote though, the Sherman was an absolute beast in the Pacific.