When did the Jewish practice of animal sacrifice cease?
My understanding is that Biblical Judaism ended with the destruction of the temple AD70.
Previous to that, at the moment of Christs' death the veil or curtain hiding the Holy of Holies was torn in two:
Matthew 27
50 Jesus, when he had cried again with a loud voice, yielded up the ghost.
51 And, behold, the veil of the temple was rent in twain from the top to the bottom; and the earth did quake, and the rocks rent;
52 And the graves were opened; and many bodies of the saints which slept arose,
53 And came out of the graves after his resurrection, and went into the holy city, and appeared unto many.
Later Paul writing to gentiles says:
Ephesians 2
12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
13 But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
14 For he is our peace, who hath made both one,
and hath broken down the middle wall of partition between us;
15 Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace;
16 And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:
17 And came and preached peace to you which were afar off, and to them that were nigh.
18 For through him we both have access by one Spirit unto the Father.
19 Now therefore ye are no more strangers and foreigners, but fellow citizens with the saints, and of the household of God;
So the Abrahamic covenant to Jew and gentile alike is now being realized with the new "religion" of Christ, the church which He purchased with His own blood - no more need of animal sacrifice (which could never save from sin anyway but a shadow of what was to come).
Around the same time-Enter Talmudic Judaism or Rabbinical Judaism, the practice of Judaism without a Temple for those who could not/would not accept "the way" of Christ.
http://en.wikipedia.org/wiki/Talmud
HankD