First of all, the Word of God emphatically tells us that we cannot inherit the guilt of other people (Deuteronomy 24:16; 2 Kings 14:6; 2 Chronicles 25:4; Ezekiel 18:20). In other words, God holds us accountable only for our sins, not those of other people. We are judged according to our conduct (Romans 14:12; 2 Corinthians 5:10; 1 Peter 1:17; Romans 14:12), not the actions of other people. God refused Moses' plea to take punishment on somebody else's behalf (Exodus 32:31-33). We are clearly held responsible for our own choices. As a matter of fact, Jesus indicated that children are in a sense better models of purity than adults (Matthew 18:1-5; 19:13-15; Mark 10:13-16). Though we have inherited a sin nature from the Fall, behaviors are learned and chosen.
So, what about the Old Testament passages that people misuse to teach the concept of generational curses? The two parallel passages recording the Ten Commandments do not say that God would give generational curses to people. Rather, God would visit their iniquity. God punishes the people who continue in their sin and rebellion against Him, and reveals mercy to all who turn to Him. Consequences can be passed on to future generations, not curses. Nobody has to be trapped in sin. The forgiveness of God and salvation is not beyond the reach of anybody. There is a "curse" only in the sense that moral corruption has been passed on to mankind because of the Fall. Atonement is available to all through faith in the Lord Jesus Christ. He bore all potential curses on our behalf (Galatians 3:13).
If we can inherit the sin of our parents, then would that also mean that we could inherit their righteousness? Can we inherit the mercy of God? The idea that people can inherit irreversible hexes or curses from their parents is both irrational and unbiblical. If one walks according to the Spirit through faith in Christ, then there is no condemnation (Romans 8:1). This generational curse nonsense has no doubt caused much unnecessary fear and anxiety in the lives of people. The Lord is faithful, rich in mercy, abounding in love, and slow to anger (Exodus 34:6; Psalm 103:8-14). Our fellowship with God has nothing to do with our family ancestry. If it did, that would make Him a respecter of persons (Acts 10:34). Nowhere does Scripture even provide us with instructions as to how to break so-called generational curses.