Following hot on the heels of Puritan Lad, I want to add some clarity around the law, and how it relates to Christians today.
There is no difference between OT law and NT law, it is the same law, just as the Gospel is the same gospel in the OT and NT. The unique function of the law is to convict us of our sin:
Romans 7:7 (NIV)
"What shall we say, then? Is the law sin? Certainly not! Indeed I would not have known what sin was except through the law. For I would not have known what coveting really was if the law had not said, "Do not covet."
Biblical law can be divided into 3 parts:
1. Civil Law - those laws that were applied to Israel to ensure the proper running of their society, and relevant to their specific place and position in history. This is where the laws regarding Israels conduct towards other nations and their traditions were, and were put in place to ensure the survival of the Israelites at that point in history. Our society today is different, therefore these laws do not specifically apply to our society today, but the principles behind them stand, as demonstrated by Jesus.
2. Ceremonial Law - related specifically to the way Israel was to worship, and pointed forward to the coming of Jesus. This is also where the Pharisees added their traditions, which were condemned by Jesus as opposed to the Commandmentss of God. While we are no longer bound by the ceremonial laws, since the prophesies regarding Jesus in this part has been fulfilled, the principles of worshipping and loving a Holy God still apply.
3. The Moral Law, such as the 10 commandments, are the direct commands of God, and should be strictly obeyed. The moral law reveals God's will and nature, and was obeyed by Jesus completely. These laws call us to righteousness, and into strict obedience, along with the acceptance of God's grace through faith in Jesus. It is not a call for legal compliance, but righteousness that comes from what God does in us, be God-centered and not self-centered, be based on worship and reverance for God, go beyond keeping the law to the principles of God's law.
We cannot know that we are in sin, and therefore in need of someone who has fulfilled the laws demands, without Biblical law. The law crushes any hope that the sinner has to reach eternal salvation, but shows the reliance we have on Jesus, the only one who could fulfill the law. The law proclaims judgment and death, the gospel justification and life through Jesus, and knowledge of the nature and charactersistics of our sin.
Jesus did not in the gospel dissolve the moral law, but strengthened it.
Matthew 5:17-20 (NIV)
"Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them.  I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished.  Anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven.  For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven."
The fulfillment Jesus speaks about here is the ceremonial law that related to Lev 17:11, which he thus fulfilled, and we are no longer subject to. He also kept God's moral law perfectly, but did not come to abolish it. In fact, He teaches that one who teaches the commands of God will be called great in heaven. The Pharisees added their traditions to the law:
Mark 7:6-8 (NIV)
He replied, "Isaiah was right when he prophesied about you hypocrites; as it is written:
" 'These people honor me with their lips,
but their hearts are far from me.
 They worship me in vain;
their teachings are but rules taught by men.'
 You have let go of the commands of God and are holding on to the traditions of men."
This is what is widely condemned throughout the NT, by Jesus and by His disciples, and is interpreted as abolishing all so-called OT law. In the ceremonial and civil law, they added to God's commandments, and therefore was called hypocrites and worse by Jesus. In fact, Paul calls these traditions "old wives tales".
So how does all of this relate to life today? How is it determined what is right and what is wrong?
God is the ultimate power over all authorities. He alone has the power and right to appoint those who will oversee His creation. The Bible talks about 4 levels of authority:
1. In the home, authority is to the husband, and together with the wife, over the children.
2. At the workplace, managers, owners or employers are given the authority.
3. In church, the elders and pastors have the authority.
4. In society, the authority is with civil governments.
Each of those have the obligation to do God's will, since they were appointed by Him. This means complying with His moral law, as described in the Bible. All of these authorities are secondary to God's will, and we are implored to do God's will first.
Civil governments rule as agents of God. They answer to God and must submit to all of His laws as they carry out their duties. No government has any authority to infringe upon the authorities given to other levels of leadership assigned in scripture in the home, work place and church, except where abuses of those endanger the civil order.
Romans 13:1 (NIV)
"Everyone must submit himself to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God."
To disobey government, is to disobey God Himself. Even the Jews found this out the hard way, when they did not submit to Roman authority, and were expelled from Rome, and ancient Jerusalem destroyed.
The Bible doesn't prescribe a specific form of government or political system. Whether its a monarchy, an empire, a republic, a social democracy, tribal elders, or a dictatorship God uses the civil authorities for his own purposes, even if they don't recognize that what they are doing fits into God's plan. God uses even our always imperfect and sometimes corrupt governments to maintain limits on social behavior, and to ensure a common peace and safety.
The duty of civil governments is clear in the Bible:
Romans 13:3-4 (NIV)
"For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and he will commend you.  For he is God's servant to do you good. But if you do wrong, be afraid, for he does not bear the sword for nothing. He is God's servant, an agent of wrath to bring punishment on the wrongdoer."
It is clear that civil governments have the God-given duty to protect citizens from evil and wrongdoing, and that those who obey the laws have nothing to fear. Civil governments must administer good in the public sphere, and keep the civil order for those who obey the laws. Those who break the laws must not only fear the justice of the civil government, but also the wrath of God.
Governments have a right to use physical force against criminals. Bearing the sword is most often connected with the execution of capital punishment. It's not murder when the state executes a convicted murderer. God's word makes murder a capital crime because of the absolute dignity of human life. This is how God ordains to carry out his wrath in this world.
So government, through its courts and under the limits of due process and the laws of evidence, are the only rightful avengers in society. No one may take the law into his own hands.
Even Paul, when under arrest, agreed with that principle as it applied to his own case:
Acts 25:11 (NIV)
"If, however, I am guilty of doing anything deserving death, I do not refuse to die. But if the charges brought against me by these Jews are not true, no one has the right to hand me over to them. I appeal to Caesar!"
We further see that Paul instructs us to submit for the sake of being wise:
1 Peter 2:13-15 (NIV)
Submit yourselves for the Lord's sake to every authority instituted among men: whether to the king, as the supreme authority,  or to governors, who are sent by him to punish those who do wrong and to commend those who do right.
For it is God's will that by doing good you should silence the ignorant talk of foolish men.
Therefore government has specific areas of proper God-given authority. They are to ensure public safety and to preserve life and property.
For example, they enact laws against: robbery, theft, assault, murder, rape, incest, perjury. For safety against irresponsible citizens they regulate traffic with speed laws, they license drivers, mandate us to register our vehicles and to keep them safe for use on the public roads.
If we think some laws are unwise, we can work to change them. But like it or not, we must obey them exactly as long as they don't require us to sin.
(Some information from the Genevan Institute for Reformed Studies)