Why does sin go unpunished?

God is the enforcer of His own holiness.  God's holy nature means He cannot let sin go unpunished.  In fact, if He could He would not only be unholy but he would be unloving to allow injustice to go unfettered.  This begs the question though: why, if God cannot let sin go unpunished do we see sin go unpunished each and every day?  The Psalmist spoke to this exact question in Psalm 73:  "For I was envious of the arrogant when I saw the prosperity of the wicked." (Psalm 73:3)

The quick answer to this question is God is patient.  He desires that all should repent and so He gives them time (2 Peter 3:9).  His patience with sin is part of His kindness which is intended to lead us to repentance (Romans 2:4).  God's patience with sin is only possible, however, because His wrath and punishment for sin was sufficiently poured out on his faultless Son through his death on the cross. Paul explains this in Romans when he says,

23 for all have sinned and fall short of the glory of God, 24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus, 25 whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins. 26 It was to show his righteousness at the present time, so that he might be just and the justifier of the one who has faith in Jesus.  Romans 3:23-26, emphasis mine

Notice Paul says God "passed over former sins" in his "divine forbearance".  "Forbearance" literally means "to delay enforcement."  So God was able to delay the enforcement of the penalty for our sins because Christ adequately satisfied God's righteousness for those who have (or will have) faith in Christ.  So God's forbearance is primarily intended to benefit those who will put faith in Christ, but it temporarily benefits those who will not put faith in Christ.  This is why 1 Timothy 4:10 says God is "the Savior of all people, and especially of those who believe."  This does not mean that all people are saved from judgement, but that judgement is graciously delayed.  All people benefit from Christ's sacrifice, but not all in the same way.