Actually, it's my understanding that the Luger was no longer issued starting in 1942, due to manufacturing costs. Prior to that, all units were issued Lugers, but during the war the Walther P-38 became the 'standard' issue sidearm. Other sidearms were used, esp. later in the war, including (but not limited to) the Browning P-35 (Hi-power), Walther PP & PPk, Polish Radom, and Mauser Hsc. It is my understanding that the higher the rank, generally the smaller the pistol, so weapons such as the PP & Hsc were carried by higher ranking members.
Interestingly enough, if you watch a fair number of war movies, you will see that the Luger & the P-38 get switched around a fair amount......in one scene the Nazi is holding a Luger; in the next, a P-38 (or vice versa).