The distinctive Nazi stahlhelm (German for "steel helmet", but generally used to refer to the specific WWII design) had its "ear protectors" (for lack of a better term) flared outward in such a way that its base was wider than the top. Did this design serve any practical purpose other than looking intimidating? I'm no mechanical engineer, but wouldn't a lack of flared base be safer (clings to the soldier's head more tightly), simpler to mass-produce, and not risk trapping a hypothetical extremely (and I do stress the word extremely) lucky shot, where the rifle flings the bullet onto the inside of the helmet just outside the combatant's ear?
The stahlhelm, developed by the Germans during the first world war, was developed after evaluating the British and French helmet designs, and then combining the strengths of each, while trying to eliminate weaknesses in either design. The stahlhelm was designed with a visor and neckguard, both of which served an important purpose.
The visor was intended to provide some relief from the elements, as well as some protection against shrapnel, while the neckguard’s main purpose was to provide protection for the neck and ears from shell fragments. According to Tubbs and Clawson in their book Stahlhelm: Evolution of the German Steel Helmet these components offered superior protection when compared to the British and French designs.
The stahlhelm went on to be the influence for most combat helmets in use today, due to the effectiveness of the design.
In short, shrapnel protection was the advantage offered by the flared neckguard.