The number one reason why we should obey Torah is because Yeshua did.  G-d provided a test through the words of the Apostle John to help us determine if we are Yeshua's followers:

By this we know that we have come to know Him, if we keep His commandments. - 1 John 2:3

Some might say that Yeshua's commandments were different from the Father's.  This cannot be... for a number of reasons.

a) Yeshua and the Father are One:

Hear, O Israel! The LORD is our God, the LORD is one! -Deuteronomy 6:4

"I and the Father are one." - John 10:30

b) Yeshua said He did not come to do his will but the will of his Father.

So Jesus said, "When you lift up the Son of Man, then you will know that I am He, and I do nothing on My own initiative, but I speak these things as the Father taught Me. - John 8:28

c) Yeshua's words are the words of the Father.

Jesus answered and said to him, "If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him and make Our abode with him. He who does not love Me does not keep My words; and the word which you hear is not Mine, but the Father's who sent Me. - John 14:23-24

d) It was Yeshua Himself who gave the Torah to Moshe and the Israelites.

Then Moses went up with Aaron, Nadab and Abihu, and seventy of the elders of Israel, and they saw the God of Israel; and under His feet there appeared to be a pavement of sapphire, as clear as the sky itself.   Yet He did not stretch out His hand against the nobles of the sons of Israel; and they saw God, and they ate and drank.  - Exodus 24:9-11

Not that anyone has seen the Father, except the One who is from God; He has seen the Father.  - John 6:46

If Exodus says they did see G-d and Yeshua says nobody has seen the Father then the only option is that Moshe, Aharon, Nadav, and Avihu saw Yeshua.  Yeshua gave the commandments at Sinai.

2) Yeshua never spoke against Torah.

Deuteronomy 13 provides a test to determine if a prophet was a true prophet or a false prophet.  If the prophet tells the Israelites to follow after some other god and disobey G-d's commandments then he is a false prophet.  Yeshua never spoke against the Torah.  If He had then He would have been a false prophet.  There are definitely times that Yeshua spoke against the traditions that had grown up around Torah and the upholding of the traditions over the commandments (e.g. Mark 7:8) but never against Torah itself.  Instead Yeshua declares that He has come to give the fullness of the Torah(Matthew 5:17)  for us to follow.

If Yeshua had ever added or removed a single commandment He would have been guilty of sin.  As it is written:

"You shall not add to the word which I am commanding you, nor take away from it, that you may keep the commandments of the LORD your God which I command you.  - Deuteronomy 4:2

Yet we know that Yeshua was without sin:

For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin. - Hebrews 4:15

Thus we know Yeshua never added to or removed a single commandment from the Sinai covenant.

3) The New Covenant is the Torah written on the heart.

The only places in Scripture where the New Covenant is explicitly mentioned and described is in Jeremiah 31 (although Hebrews 8 contains quotes from Jeremiah 31).  What does Jeremiah 31 tell us about the New Covenant?

a) The New Covenant will be made with the children of Israel (Jeremiah 31:31).  If anyone becomes a part of the New Covenant then they are first adopted into the family of Israel (as Paul states in Romans 8:15, 9:4, and Ephesians 1:5) and become inheritors of the covenant.  Not heirs according to the flesh but according to the promise (Galatians 3:29).

b) The New Covenant is the Torah (the same Torah that was written on tablets of stone) written upon our hearts (Jeremiah 31:33).  Paul states it clearly.  The same words written on tablets of stone bring death and yet when those words are written upon the tablets of our heart by the Spirit they bring life (2 Corinthians 3:1-6).

c) All who are in the New Covenant will know G-d intimately (Jeremiah 31:34).

d) G-d will forgive the sins of those in the New Covenant (Jeremiah 31:34).  Yeshua tells us it was his blood that marked the New Covenant (Luke 22:20) for the forgiveness of sins (Matthew 26:28).  So we know that there aren't two "New Covenants".  Messiah died once for all (Hebrews 7:27).

The conclusion, when all has been heard, is: fear God and keep His commandments, because this applies to every person.  - Ecclesiastes 12:13

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