No, God says in the Bible quite specifically that he does not:
Deu 24:16 The fathers shall not be put to death for the children, neither shall the children be put to death for the fathers: every man shall be put to death for his own sin.
This is repeated just to make certain we get the message:
2Ch 25:4 But he slew not their children, but did as it is written in the law in the book of Moses, where the LORD commanded, saying, The fathers shall not die for the children, neither shall the children die for the fathers, but every man shall die for his own sin.
This is repeated in the New Testament:
Joh 9:1-3 KJV And as Jesus passed by, he saw a man which was blind from his birth. [v.2] And his disciples asked him, saying, Master, who did sin, this man, or his parents, that he was born blind? [v. 3] Jesus answered, Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him.
A particular sin or crime
that has been committed is
not passed on from one generation to the next.
However, the tendency to commit a particular type of sin or crime
is passed on from one generation to the next because it is learned behavior. What
is passed on from one generation to the next is the father's attitude toward committing a particular sin and the strong likelihood of passing this learned behavior on to his son (or daughter). For example, if the father is a drunkard his son may be inclined towards alcoholism. Children learn what is acceptable behavior from their parents, and it is
not what they
say: it is what they actually do: actions always speak louder than words.