Psalm 32 - This Psalm penned by David expresses the joy and peace a repentant sinner has after they have confessed their sin(s) to God. David found that God's hand of conviction can be very heavy and he knew he would not find peace until he was open and honest before His Savior. David knew what it was like to be stubborn, but he was also grateful that God pressed him to speak up and unburden his heart before the Lord. Read this Psalm often and ask God to convict you of anything that is offensive to Him.
Psalm 51 - David wrote this Psalm as a direct result of his sin with Bathsheba and his sin against Uriah. David's expression that he sinned against God, and God only, is his way of recognizing the awful offense God takes to our transgressions. David asked that the Holy Spirit wouldn't be taken from him because in Old Testament times the Spirit did not have the same relationship with believers and He does now. God will never take the Holy Spirit away from a Christian.
Psalm 86 - This Psalm speaks of God's compassion and forgiveness to sorrowful sinners. God is good and ready to forgive all who would be open and honest with Him. If you're hiding anything, don't think God can't see your heart! He is ready to forgive you too!
Psalm 122 - This Psalm reminds us of the importance of Jerusalem. Praying for the peace of Jerusalem (verse 6) means to pray that the Prince of Peace will come and reign in that city whose meaning is, "the city of peace!"