Does the New Testament override the Old Testament? Throughout the Old Testament there have been many laws laid down by the Lord, that are perhaps more harsh then we, as Christians, follow today. Many times in the New Testament it has been found to change the laws of the Old Testament. My question is does the New Testament override the Old Testament in creating laws, that we as Christians should follow.

Old Testament:
Exodus 21:24


  eye for eye, tooth for tooth, hand for hand, foot for foot,


Then later in the New Testament: Matthew 5:38-48


  38 “You have heard that it was said, ‘Eye for eye, and tooth for tooth.’ 39 But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also. 40 And if anyone wants to sue you and take your shirt, hand over your coat as well. 41 If anyone forces you to go one mile, go with them two miles. 42 Give to the one who asks you, and do not turn away from the one who wants to borrow from you.


These two obviously conflict each other. So I ask again. 
Does the New Testament override the old?
You can find your answer a few verses earlier in the same chapter:


  Matthew 5:17-18
  
  17 Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfill.
  
  18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.


The Law of Moses was given to point people's minds forward to Jesus Christ, the promised Messiah-to-come.  Once he did come, the Law's purpose was fulfilled, and it became obsolete.  It was not destroyed, but superseded by a higher law, the law of the Gospel.