Do the Ten Commandments still apply today?

Every year at this time we make a point of watching the Cecil B. De Mille movie, "The Ten Commandments" but just how much do we know about them? When were the Ten Commandments first applied? Did they start with Moses at Mt. Sinai or does the bible show someone before Moses obeyed them? Do you only have to obey some of them or all of them? Do they apply to Christians today?

Exodus 20:1-17

(1) And God spake all these words, saying,
(2) I am the LORD thy God, which have brought thee out of the land of Egypt, out of the house of bondage.
(3) Thou shalt have no other gods before me.

(4) Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth:
(5) Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me;
(6) And shewing mercy unto thousands of them that love me, and keep my commandments.

(7) Thou shalt not take the name of the LORD thy God in vain; for the LORD will not hold him guiltless that taketh his name in vain.

(8) Remember the sabbath day, to keep it holy.
(9) Six days shalt thou labour, and do all thy work:
(10) But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:
(11) For in six days the LORD made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the LORD blessed the sabbath day, and hallowed it.

(12) Honour thy father and thy mother: that thy days may be long upon the land which the LORD thy God giveth thee.

(13) Thou shalt not kill.

(14) Thou shalt not commit adultery.

(15) Thou shalt not steal.

(16) Thou shalt not bear false witness against thy neighbour.

(17) Thou shalt not covet thy neighbour's house, thou shalt not covet thy neighbour's wife, nor his manservant, nor his maidservant, nor his ox, nor his ass, nor any thing that is thy neighbour's.

New Testament References
to Keep the Commandments

Matthew 19:17 (KJV) And he said unto him, Why callest thou me good? there is none good but one, that is, God: but if thou wilt enter into life, keep the commandments.

John 14:15 (KJV) If ye love me, keep my commandments.

John 14:21 (KJV) He that hath my commandments, and keepeth them, he it is that loveth me: and he that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him.

John 15:10 (KJV) If ye keep my commandments, ye shall abide in my love; even as I have kept my Father's commandments, and abide in his love.

Matthew 5:17-19 (KJV) Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. (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. (19) Whosoever therefore shall break one of these least commandments, and shall teach men so, he shall be called the least in the kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the kingdom of heaven.

1 John 2:3-4 (KJV) And hereby we do know that we know him, if we keep his commandments. (4) He that saith, I know him, and keepeth not his commandments, is a liar, and the truth is not in him.