Many inhabitants of the eastern portions of the Soviet Union, such as the Baltic States and Ukraine, openly welcomed the German army as their liberator and collaborated fully with it, until they discovered that German occupation policies were even more repressive than Soviet rule had been. In 1943 alone, as Soviet troops moved westward, the Soviet secret police, or NKVD, arrested more than 931,000 people for questioning. Hundreds of thousands of Soviet minorities—most notably the Crimean Tartars but also Turks and Chechens, among others—were simply deported en masse to the eastern USSR as a consequence of their wartime collaboration with the Germans. General Andrei Vlasov, a Hero of the Soviet Union, agreed to head the German-sponsored Russian Liberation Army, although Hitler refused to allow it any real function. Hundreds of thousands of Soviet prisoners worked in the German army in nonmilitary roles, as cooks, drivers, and the like. Much of their motivation came from the simple desire to stay alive, as millions of Soviet soldiers perished from starvation in German POW camps.
One tragic episode following the war resulted from the decision by the Western powers to hand over to the USSR millions of Soviet citizens, many of whom had lived in the West for decades and had played no wartime collaborative role. Nonetheless, they were shipped off to work at hard labor in the gulags.
According to George Nafziger somewhere in the region of a quarter of the entire German Army in 1945 were former citizens of the Soviet Union. He also states that around the time of D-Day something like 800,000 were in the army and a further 100,000 divided between the Kreigsmarine and Navy. These figures unfortunately aren't broken down into nationalities but it’s hard to imagine that there wouldn't be a significant number of Russians in those ranks.
Its also worth noting that when Hitler went into one of his rages about desertion rates in Vlasov's army he insisted on it being dissolved it on masse. His generals pleaded with him not to do so since the loss of all the Russian troops and Hiwis would bring the Russian front to collapse. He eventually relented to only disbanding units whose loyalty was questionable and transferring many of the others to the west. This lead to the Western Allies running into all kinds of unusual "Ost" troops in the Normandy campaign.