Actually, yes. The Airborne during the invasion of Normandy for "DDay" were ordered to not take prisoners. This was because there were obviously no facilities, or easy way to do it, when you were surrounded behind enemy lines. Beevor mentions this, and other similar incidents in his "DDay" book. One of the other incidents was using German prisoners as human shields when moving towards German positions. When the Germans opened fire it was hoped that the German POWs in front would get shot first and allow the Allied soldiers time to take cover.

According to the book Band of Brothers airborne units were ordered to not take prisoners on D-Day as a matter of practicality. They'd be fighting behind enemy lines and not knowing when they'd be relieved potentially have to hold out against who knows what in the meantime. Having to keep control of prisoners in the midst of it all would've hindered their effectiveness and may have even jeopardised the operation (the operation would go on relatively smoothly all things considered but they had no way of knowing that at the time). Elsewhere in the European Theatre there were killings of German prisoners and refusals to take prisoners in reprisal for the Malmedy Massacre (around 80 US POWs killed by a Waffen SS unit) during the Battle of the Bulge, but I'm not sure to what extent this was an 'official' order and how widely this occurred. Towards the end of the war there was a bitter hatred of the SS due to mainly to Malmedy and other atrocities and SS men were often not taken prisoner, though again I'm not sure to what extent this happened and if it was an 'official' order as such.

The Pacific Theatre was where this sort of thing most frequently occurred, Japanese troops were taken prisoner though the number was very few compared to POWs of other combatant nations. Many fighting units were often not 'required' to take prisoners. This was due to a combination of many things: extensive dehumanization of the Japanese through propaganda, reprisal for Japanese atrocities (in particular, what they themselves did to prisoners), general unwillingness for Japanese troops to surrender, possibility for Japanese soldiers to fake surrender and attack troops attempting to capture them and combat often occurring in environments where prisoners could not be easily kept under check or sent to the rear (ie, small units in jungle environments). The sad thing is due to all this a lot of men who probably would've given up peacefully and survive the war felt compelled to fight to the death, as they legitimately believed not only would they dishonour themselves in surrendering but they would just be killed anyway.