Romans 3:1-8 is the Biblical answer to those who want to blame God for their sins or those who want to say they didn't have the opportunity that someone else may have had to know God. Our unrighteousness serves to show God's righteousness. If our sin leads to the glory of God and His righteousness, it doesn't mean that sin is okay or that the sin itself glorified God. It's the fact that sin can point to other attributes of God's righteousness and holiness. We will still pay the consequences for our sins and without Christ we would die for eternity in Hell.
I think this section of scripture is for people who are more philosophical than I am. I can't really get my mind to think that God is responsible for sin. I can agree that He allows it. I can agree that He orchestrates events that lead men to sin and that he uses man's sins to bring glory to Himself and work out His will and plan. But God is holy, perfect, pure. He does not sin and does not allow sin in His presence. Sin points to how complete and perfect His holiness and righteousness are. Sin also allows us to understand His mercy, grace, and love.
Praise God for His Righteousness.