Could Germany have won? Yes. The odds against Germany were pretty steep though.
With Major Shifts from History
An easy win would have required several major alterations of history including a war production board aligning Germany's economy for war; a greater emphasis on motorization and logistical transport/tank recovery units; discarding the use of naval surface vessels past those needed for service strictly in the Baltic so as to greatly increase the numbers of submarines and reprovisioning submarines available; a far greater effort to neutralize/conquer Gibraltar and Malta; A greater willingness to turn the panzer spearheads loose without worrying about their flanks so as to multiply the speed/shock impact; and under no circumstances declare war against the USA until after they have declared war on you. Just a few minor things.....
Without
Absent major changes from what happened, it is possible, though still a bit unlikely, that Germany might have punched through to Moscow -- with it's attendant destruction of a big slice of Soviet heavy industry and their rail infrastructure -- had the Germans followed the conquest of Smolensk with short operational pause and a direct strike at the Soviet capitol (beginning c. 15 Sep not 2 Oct). Would have been tough going logistically, but might have brought Stalin's regime down and/or shattered the entire front as the rail network went down for everything North of Vorozneh [sic?]. Apparently, Sep/Oct of '41 was the only time the Russians were truly on the brink of an outright collapse. The Caucuses campaign in '42 was hard on the Soviets, but never brought them to the brink of collapse.
And yes, ultimately, it all hinged on Russia. Had Germany won there it would have been almost impossible for the USA/UK to retake Europe. With Atomic weapons years away -- and some worried it was many years yet at the time -- it is arguable that some form of peace deal could have been made that left Germany in charge of pretty much all of Europe East of the Rhine.
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