So, does God actually punish people for the sins of their fathers?
Being a Star Trek fan the first thing that popped into my head was how Klingons do shame children for the sins of their fathers and in one episode Captain Picard refused to judge Duras for the sins of his father, like the Klingon empire did to Worf. (I hope I didn't sound like too much of a nerd there)

So the first verse that came out was Exodus 20:5 "fyou shall not bow down to them nor 2 serve them. For I, the LORD your God, am a jealous God, visiting the iniquity of the fathers upon the children to the third and fourth generations of those who hate Me" This is a tough one isn't it? What do we do with this verse? Because we also have verses such as:
Ezekiel 18:20 "The soul who sins shall die. The son shall not bear the guilt of the father, nor the father bear the guilt of the son. The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself." It doesn't get much clearer than this, that we are responsible for ourselves, and we will not be held responsible for the sins of our parents. We also have many more verses to support the idea that God does not punish for the sins of the parents but Ill just concentrate on these two verses.
It was then presented to me after these two verses that this was an obvious "Bible contradiction" so we have to look into it because if the Bible does actually contradict itself we have a very big problem on our Christian hands. So lets have a look.
The context of Exodus 20 is the practice of idolatry. This section of scripture is speaking towards consequences of sin, not necessarily punishment from God. Are there consequences to sin that do follow down through generations? Of course there are. I think of divorce for example. Divorce can cause a wake

Yet, anyone who could be effected by the consequences of the sins of their parents can turn to Jesus, who was perfect and had no sin, actually was put to death on a cross as a ransom for our sin. Anyone can come to Jesus and the sins of their parents would not be held against them at all.(Corinthians 5:21) Anyone who comes to Jesus in faith is considered righteous in the sight of God and can know God.

Personally one of my favourite things about God is that he really can make all things new (Revelation 21:5) and really can restore the lost years. Personally I know many people who are hurt by the sins of their parents, and I am not going to tell you it will be all better if you come to Jesus, it will still be a long tough road. But Jesus will stand with you and forgive you and work together with you.
So, does God punish people for the sins of their parents? No. Is there such a thing as generational curses or the like? No. Can children's lives be effected by the sins of their parents? Yes. Are there consequences to sin? Yes. Can God restore, heal and forgive all sin? Yes.