Well, in many areas crucifixion victims were denied proper burial: they were simply left to rot on their crosses or eventually dumped into some garbage heap somewhere. That was a part of the shame of crucifixion.
But in Judaea, the Jews made (and even today, still make) a big deal about burying dead bodies, even those of total strangers. Deuteronomy 21 says:
When someone is convicted of a crime punishable by death and is executed, and you hang him on a tree, his corpse must not remain all night upon the tree; you shall bury him that same day, for anyone hung on a tree is under God’s curse. You must not defile the land that the LORD your God is giving you for possession.
It is because of this command in Deuteronomy that some think that the Jews were granted a concession from the normal practice of crucifixion. Instead, it could be more likely that in Palestine, crucified victims were allowed to be buried as soon they were dead. Unlike in other parts, leaving the bodies unburied would have been more the exception rather than the rule. The historian Josephus in one place even said that “the Jews used to take so much care of the burial of men, that they took down those that were condemned and crucified, and buried them before the going down of the sun” (War 4.317).
Craig Evans in his article Jewish Burial Traditions and the Resurrection of Jesus points out:
The Digesta [a summary of Roman law] refers to requests to take down bodies of the crucified. Josephus himself makes this request of Titus (Life 75 §420–421). Of course, Roman crucifixion often did not permit burial, request or no request. Non-burial was part of the horror—and the deterrent—of crucifixion. But crucifixion—during peacetime—just outside the walls of Jerusalem was another matter. Burial would have been expected, even demanded. The evidence thus far reviewed strongly encourages us to think that in all probability Jesus was indeed buried and that his corpse and those of the two men crucified with him would not have been left hanging overnight and perhaps indefinitely, or at most cast into a ditch or shallow grave, exposed to animals. Quite apart from any concerns with the deceased men or their families, the major concern would have had to do with the defilement of the land and the holy city. Politically, too, it seems unlikely that on the eve of Passover, a holiday that celebrates Israel’s liberation from foreign domination, Pilate would have wanted to provoke the Jewish population. Moreover, it is equally improbable that the ruling priests, who had called for Jesus’ death, would have wanted to appear completely indifferent to Jewish sensitivities, either with respect to the dead or with respect to corpse impurity and defilement of the land. It seems most probable that the priests would have raised no objections to the burial of the three men. Indeed, they probably would have arranged to have them buried, before nightfall, in tombs reserved for executed criminals.