"Think not that I have come to abolish the law and the prophets; I have come not to abolish them but to fulfil them. For truly, I say to you, till heaven and earth pass away, not an iota, not a dot, will pass from the law until all is accomplished. Whoever then relaxes one of the least of these Commandments and teaches men so, shall be called least in the kingdom of heaven; but he who does them and teaches them shall be called great in the kingdom of heaven. For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven." (Matthew 5:17-20 RSV)
Jesus Did Not Break The Law
As the Scriptures above make plain, Jesus Christ was not a radical, or a law breaker. And yet, He was frequently accused of being so:
"And behold, some of the scribes said to themselves, "This man is blaspheming." (Matthew 9:3 RSV)
"Look, Your disciples are doing what is not lawful to do on the Sabbath." (Matthew 12:2 RSV)
"And they asked Him, "Is it lawful to heal on the Sabbath?" so that they might accuse Him." (Matthew 12:10 RSV)
"Why does He eat with tax collectors and sinners?" (Mark 2:16 RSV)
Whose Law?
God formally gave His Law to the Israelites, through Moses, during the Wilderness Journey after the Exodus. This is what Jesus was referring to in the opening paragraph. God's Law was observed by Jesus perfectly, since Jesus never sinned (see What Is Sin?).
After their entry into the Promised Land under Joshua, the Israelites became increasingly corrupt in their obedience to God's Law. Because of their forsaking of Him, God eventually permitted the two kingdoms (after the death of Solomon, when his son Rehoboam began to reign, the United Kingdom of Israel split into two separate Kingdoms, "Israel" and "Judah," and were never united again) to be destroyed.
First, the northern kingdom of Israel was gradually conquered by the Assyrians (see Ancient Empires - Assyria), and by 721 B.C. they had practically all been taken into exile to Assyria (2 Kings 17:1-23). The vast majority of them never returned, and have become known as the "Lost Ten Tribes of Israel."
Then, about 135 years later, in 586 B.C., the southern kingdom of Judah was conquered by the Babylonians (see Why Babylon? and Ancient Empires - Babylon), and the Jews (the northern kingdom of Israel, the northern ten tribes, were not Jews, since only the descendants of Judah, with Benjamin included, are Jews - see Hebrew) were taken into captivity to Babylon. The original Temple of God in Jerusalem was destroyed at that time (see Temples and Temple Mount Treasures). The people of the southern kingdom of Judah however did return after the Babylonians fell to the Persians (see Ancient Empires - Persia), and their descendants have become the Jewish people of today.
Upon their return from the Babylonian captivity, the religious leadership vowed never again to allow the people to disobey God's Law so as to bring His wrath upon them. That was very good, except that in their zealousness to obey God's Law, they added many of their own laws - traditions and customs were gradually added by authorities such as the Pharisees and Sadducees - "laws" that none of the righteous patriarchs, including Abraham, Isaac and Jacob - or Moses himself, ever knew or observed.
By the time of Jesus Christ, the man-made laws and traditions were viewed nearly on the same level as God's actual Law - and it was for this that Jesus rebuked them for worshiping God according to their own traditions:
"Now when the Pharisees gathered together to Him, with some of the scribes, who had come from Jerusalem, they saw that some of His disciples ate with hands defiled, that is, unwashed. For the Pharisees, and all the Jews, do not eat unless they wash their hands, observing the tradition of the elders; and when they come from the market place, they do not eat unless they purify themselves; and there are many other traditions which they observe, the washing of cups and pots and vessels of bronze. And the Pharisees and the scribes asked Him, "Why do Your disciples not live according to the tradition of the elders, but eat with hands defiled?" And He said to them, "Well did Isaiah prophesy of you hypocrites, as it is written, 'This people honors Me with their lips, but their heart is far from Me; in vain do they worship Me, teaching as doctrines the precepts of men.' You leave the Commandment of God, and hold fast the tradition of men." And He said to them, "You have a fine way of rejecting the Commandment of God, in order to keep your tradition!" (Mark 7:1-9 RSV)
"And in His teaching He said, "Beware of the scribes, who like to go about in long robes, and to have salutations in the market places and the best seats in the synagogues and the places of honor at feasts, who devour widows' houses and for a pretense make long prayers. They will receive the greater condemnation." (Mark 12:38 RSV)
Fact Finder: Are Christians to observe The Ten Commandments? See The Ten Commandments Now?