Are people punished for the sins of their fathers?
God is very clear about holding individuals accountable for what they have done. Romans 14:12 reminds us that "each of us shall give an account of himself to God." Our personal accountability for sin is precisely the reason that God sent Christ, so that He could pay the penalty for our sin (Isaiah 53:6).
The theme of personal accountability is consistent throughout Scripture, and the result of sin is twofold: Earthly consequences of sin, which often extend "to the third and fourth generations"; and eternal judgment for sin, which applies only to the person committing the sin. The passages you mention in no way contradict each other or conflict with these principles.
Sins such as divorce, alcoholism, sexual abuse, to name a few, have repercussions that ripple out for many generations. The passage in Numbers is a warning that what we do now continues to make an impact long after we're gone.
Also, read the passage carefully and you see that the Bible doesn't say that children are punished for their father's sins, but for sins which their fathers committed - and which they repeated. Sadly, sin habits often tend to be passed down from generation to generation. God's punishment is actually the Father's loving action to help stop the chain-reaction suffering that sin produces.
Taken from Adrian Rogers' weekly newspaper column. Used by permission. © 2001, The Commercial Appeal.