The short answer is yes, in some circumstances, he does. I think we see this in scripture three ways. The first way is through the federal headship of Adam. In this way, all human beings come into the world guilty of Adam’s sin:
For as in Adam all die, so also in Christ shall all be made alive. – I Corinthians 15:22
This circumstance is unique in that Adam and Adam alone is the federal head for humanity. No other human being since has fulfilled this role.
The second way is via the method of sowing and reaping that God has built into his creation:
You shall not bow down to them or serve them, for I the Lord your God am a jealous God, visiting the iniquity of the fathers on the children to the third and the fourth generation of those who hate me, but showing steadfast love to thousands of those who love me and keep my commandments. – Exodus 20:5-6
Notice this is not judgment for a specific sin but a promise of an outcome for the offspring of those who hate the Lord. This is not a hard-and-fast promise any more than Proverbs 22:6 is a promise that children of godly parents will never stray. It is recognition that when people reject God that will have implications for their children, grandchildren and beyond.
In the third way, God issues a direct command to his people to mete out justice on certain people he has identified and holds responsible for specific acts of their ancestors:
“No Ammonite or Moabite may enter the assembly of the Lord. Even to the tenth generation, none of them may enter the assembly of the Lord forever, because they did not meet you with bread and with water on the way, when you came out of Egypt, and because they hired against you Balaam the son of Beor from Pethor of Mesopotamia, to curse you. But the Lord your God would not listen to Balaam; instead the Lord your God turned the curse into a blessing for you, because the Lord your God loved you. You shall not seek their peace or their prosperity all your days forever. – Deuteronomy 23:3-6
Here, the Lord calls out the Moabites for failing to provide for the physical needs of Israel after the Exodus and trying to curse them. The punishment is that no Moabite can enter the assembly of the Lord for ten generations. Additionally, the Israelites are commanded never to seek the peace or prosperity of a Moabite.
Later in the passage we read:
“You shall not abhor an Edomite, for he is your brother. You shall not abhor an Egyptian, because you were a sojourner in his land. Children born to them in the third generation may enter the assembly of the Lord. – Deuteronomy 23:7-8
Edom who also mistreated Israel and even Egypt who enslaved them for four hundred years are not to be abhorred and their descendants may enter the assembly of the Lord in the third generation.
Or consider this:
Thus says the Lord of hosts, ‘I have noted what Amalek did to Israel in opposing them on the way when they came up out of Egypt. Now go and strike Amalek and devote to destruction all that they have. Do not spare them, but kill both man and woman, child and infant, ox and sheep, camel and donkey.’ – I Samuel 15:2-3
Because of what their ancestors had done to God’s people hundreds of years before, Saul was commanded to wipe out the Amalekites living in his day including women, children and even their animals.
How are the guilty parties determined in these cases and why the differing punishments? From our perspective four hundred years of slavery seems a worse offense than failure to provide supplies along the road, yet God is more merciful to the Egyptians than to the Moabites. Likewise, killing every living thing in a city for sins committed hundreds of years ago seems quite harsh to our modern ears. We often don’t know why God does what he does unless he chooses to tell us. What we do know is that God is perfect in all his attributes so any pronouncement from him, any punishment he prescribes, is good and right and just.
So, yes, God, in certain circumstances, holds people accountable for the sins of those who lived before them. But there’s a second question to consider. Does that mean we can do the same? Can we make the decision either personally or via the authorities God has ordained to assign guilt to people in the present for offenses committed by their ancestors and then prescribe the punishment they are to receive?
Here I believe the answer is no – because we’re not God.
In each of the cases above, guilt was assigned and the punishment determined by God himself and communicated via direct revelation. The descendants of the victims didn’t decide who should be punished and how, God did. We don’t possess God’s omniscience or his ability to read the human heart. Therefore, God has given us a framework to use for making decisions in a manner consistent with his justice. Within that framework, we are prohibited from punishing people for the sins of their ancestors or their offspring:
“Fathers shall not be put to death because of their children, nor shall children be put to death because of their fathers. Each one shall be put to death for his own sin. – Deuteronomy 24:16
Notice this is the very next chapter after God instructs his people to bar Moabites from the worship of the Lord for ten generations because of the actions of their “fathers.” The admonition against punishing children for the sins of their fathers is repeated in Ezekiel 18:20.
King Amaziah, one of Judah’s godly rulers, understood this:
And as soon as the royal power was firmly in his hand, he struck down his servants who had struck down the king his father. But he did not put to death the children of the murderers, according to what is written in the Book of the Law of Moses, where the Lord commanded, “Fathers shall not be put to death because of their children, nor shall children be put to death because of their fathers. But each one shall die for his own sin.” – II Kings 14:5-6
Amaziah knew that, as king, his power and authority were limited by the commands of God and therefore he did not have the authority to punish the next generation for the sins of their fathers.
Simply put, God can do things we cannot do. For example, in Acts chapter five, the Lord deals with sin in the church by killing two people. We, however, have no such authority. We are to deal with sin in the church using the framework God has provided in Matthew 18:15-20 and other places.
In the end the sin we should most be concerned about is our own. Beyond that, as we engage with culture and each other, we should seek justice within the framework prescribed by God and leave the things outside that framework in the hands of the One who has promised that, in the end, no sin will go unpunished.