In 1940, before the U.S. joined the war, Look magazine presented Shuster and Seigel's take on how Superman might influence world events.  Remember that at this point, the non-aggression pact between Hitler and Stalin remained intact.

Many superheroes of the Golden Age took on the Axis leaders. On the cover of Superman #17, at left, our non-Nietzschean Superman takes on Adolf Hitler and Emperor Hirohito.
Superman's principal rival, Captain Marvel, uses an "honesty ray" on three chief Nazis leaders on this cover.

In reality, the war would wage for some time, and the comics had to adjust to that fact. One early issue even had the services reject Clark Kent (and therefore Superman), because his x-ray vision led him to read the wrong eye-chart!

Years later,
DC Special #29 (1977, above), explained the failure of the Justice Society to bring an immediate end to the war on Earth-2, where the Golden Age heroes resided and Superman made his debut in 1938. Hitler, obsessed with mystic relics, used the "Spear of Destiny," which allowed him to control any metahuman who entered Axis territory. The battle doesn't fall entirely in Hitler's favour, however; the Spectre pretty much single-handedly prevents a Nazi invasion of England. A variation of this story also appeared post-Crisis, in Secret Origins #31.

Captain America, of course, was a natural to take on Der Fuhrer.