They may not goose-step around the Death Star, but Imperial stormtroopers are heavily inspired by German stormtroopers. Go figure, right? It makes sense, as George Lucas once explained to the Boston Globe in 2005 (via The History Channel), "I love history … so while the psychological basis of Star Wars is mythological, the political and social bases are historical." In particular, much like BFF Steven Spielberg, Lucas has a major fascination with World War II.
During WWI, Germany used small units of soldiers called Sturmabteilung, or "storm troops," to break through enemy lines using stealthy tactics and brute force. During the early '20s, Hitler re-purposed the "storm troops" into a military group called the SA, which he used as protection during party meetings, and as a disruption to opposing political groups. Known for their brown shirts and black jackboots, the often violent SA were heavily featured in both pro and anti-fascist propaganda and became "the face" of Nazi Germany.
These "brown shirts" have much in common with their Imperial "bucket-head" offshoots, whether spreading fear to all around them or displaying an unwavering allegiance to their leader no matter how crazy and violent his ideas. And let's be real, Palpatine had to be crazy, to have built an expensive, moon-sized, planet-destroying weapon/base … twice. Ah well, loyalty is blind … at least when it's wearing those cumbersome white helmets.