In Ezekiel 18, I find God teaching the nation of Israel about the proper use of a proverb relating to this very thing. From v. 2, "The fathers have eaten sour grapes, and the children's teeth are set on edge", I believe the people were construing this proverb to mean that they were being punished for the sins of future generations and were thus feeling hopeless. After all, if they thought they were going to be punished anyway for something they didn't do, why behave, right?
God spends the rest of the chapter explaining to them the true meaning of the proverb, that while we have to live through the consequences of the sins of those before us, we will only "die" for our own sins. That is a comforting fact.
My favorite part of the chapter was at the end where God tells us that He really doesn't like to exact His judgment on us.
"Therefore I will judge you, O house of Israel, every one according to his ways," says the Lord God. "Repent, and turn from all your transgressions, so that iniquity will not be your ruin. Cast away from you all the transgressions which you have committed, and get yourselves a new heart and a new spirit. For why should you die, O house of Israel? For I have no pleasure in the death of one who dies," says the Lord God. "Therefore turn and live!"