Depends on what front they were on, and the circumstances of his capture. The Eastern Front was notorious for being completely brutal, largely due to the ideological indoctrination each side had endured. The Germans were taught that the Russian and Soviet people were subhuman and were worthy of being treaty like cattle and killed indiscriminately. The Soviets had endured years of German terror, murder and atrocity, and had been indoctrinated and encouraged by their own side to "take their revenge". Accounts of arbitrary shootings were common on both sides. Accounts from Soviet soldiers can attest to this

"We killed soldiers just like that (snapping his finers), if soldiers were told to escort them to the rear, more often then not the were "shot while trying to escape." -Captain Vasily Krylov.

On the Eastern Front, it was safest to surrender en masse in order to maximize your chances of survival. Surrendering as part of a larger group, such as the German 6th Army in Stalingrad, would mean it would be harder for your captors to kill you while escaping outside scrutiny. Most outright killings happened on a small scale basis, motivated by individual actions or small groups (there are, as always, distinct exceptions to this). Most captures on the Eastern front on the small scale where primarily for intelligence gathering, what the Soviets called Yazik, or tongues.

On the Western Front, your chances were much better on both sides. However, it was, as always, dependent on the circumstances. Allied airmen had a high rate of being killed after being captured, supposedly due to the anger of ground troops who retaliated against airmen because of the feelings of completely helplessness they felt when under air attack. The 1st SS Panzer Liebstandarte, killed many American captives during the Ardennes offensive, which lead to American's refusing to take SS captives. Often certain units took on reputations for not taking prisoners, such as some of the Polish attachments to the Western Allied Armies.

In summary, it is largely up to the circumstances of the capture. In the East, it was more likely you were going to be shot outright, but in the west, your chances where much better, particularly if you were not part of the SS

Source: Hastings, Max. Armageddon: The Battle for Germany, 1944-45. New York: A.A. Knopf, 2004.