(covers information from several alternate timelines)
The Schutzstaffel, or SS, was a paramilitary organization which existed as the armed branch of the Nazi political party in Germany from the late 1920s until the collapse of Nazi Germany in 1945. It was formed at first to be a special guard for Adolf Hitler and was known in the 1930s for its distinct black uniforms, and on both Earth and Ekos for the brutality and cruelty of their tactics, including torture.
The German SS
The SS was based on a racial ideology which stated that the German people were destined to be masters of Europe. Germany was superior to all other nations, so believed the SS, and it was the duty of the SS to purge the German lands of inferior peoples and "cleanse the German blood". To this end, the SS became the primary organization in persecuting the Jewish people which were seen as inferior and mortal enemies of Germany. (VOY: "The Killing Game")
During the Second World War, the SS became an elite unit, with field SS units wearing field grey uniforms instead of black. Like their '30s counterparts however, the World War II SS was easily identified by "SS bolts" on the collars of their uniforms, accompanying their rank insignia. The SS was not beyond committing war crimes, such as indiscriminately rounding up civilians or torturing prisoners. (ENT: "Storm Front", "Storm Front, Part II")
In an alternate timeline, Germany was assisted in its war by the Na'kuhl and invaded the east coast of the United States. The Na'kuhl, led by Vosk, were granted membership in the SS complete with the right to wear SS uniforms and several Nazi military decorations. Vosk became a senior SS officer, granted the rank of obersturmbannführer. In that version of history, the (non-Na'kuhl) SS was tasked with maintaining security in occupied America with SS security squads patrolling the streets of such major cities as Washington, DC and New York City. (ENT: "Zero Hour", "Storm Front", "Storm Front, Part II")
When the Hirogen captured the USS Voyager, and programmed the holodeck with a World War II scenario, several holodeck characters were portrayed as members of the SS during the years of the French occupation. The Hirogen interacted with the SS and the Hirogen leaders posed as senior SS officers. (VOY: "The Killing Game", "The Killing Game, Part II")
The concept of German racial superiority was seen as a falsehood by the Hirogen with Karr questioning one of the holodeck SS characters on the subject and determining that, without their weapons to back them up, the SS were just the same as their victims. The German arguments of racial superiority upset Karr, and he exclaimed to an SS-Hauptsturmfuehrer: "You are superior to NO ONE!"
The Ekosian SS
A resurgence of the SS began on the planet Ekos in the 2260s under the guidance of Federation historian John Gill. In a social experiment, Gill created an equivalent of the Nazi party which soon became the governing body of Ekos. Gill also formed an SS whose officers employed similar procedures and policies as the original organization. Gill's original intention was to have both the Nazi Party and the SS function as passive organizations, for the good of Ekos, but a plot by Gill's subordinate Melakon derailed this plan and the SS soon turned into a brutal organization which persecuted the Zeon minority on Ekos.
The Ekosian SS used torture and execution and openly engaged in genocide after Nazi policies turned towards purging Ekos of all Zeons. The SS shot down Zeons in the streets of Ekosian cities, spitting on the wounded and dying, and typically executed prisoners suspected of crimes. (TOS: "Patterns of Force")