God gives us two very good reasons in Scripture for why we should forgive. First, God commands us to forgive others. God forgave us while we were His enemies (Romans 5:10), and we should do likewise with one another. Second, those who do not forgive others indicate that they themselves have not been forgiven because a truly regenerated heart is a forgiving heart (Matthew 6:14-15). If we are filled with resentment and bitterness, we are exhibiting the "works of the flesh," not the fruit of the Spirit which is evidence of true salvation (Galatians 5:19-23).
Most importantly, when we disobey one of God's commands, such as the command to forgive, we sin against Him. In refusing to forgive another person, we sin against that person, but also against God. Considering that God puts our transgressions as far from Him as the east is from the west (Psalm 103:12), He expects us to extend this same grace to others. Our sin against God is infinitely more egregious than anything another person can do to us. Jesus' parable of the unforgiving servant (Matthew 18:23-35) illustrates this truth. The servant had been forgiven a massive debt—symbolic of the debt of sin we owe to God—then refused to forgive a minor debt of a friend. The lesson of the parable is that if God's forgiveness toward us is limitless, so should ours be limitless toward others (Luke 17:3-4).