Answer:
   
   It is important to note that in Judaism, sacrifice was never the
   exclusive means of obtaining forgiveness, and was not in and of itself
   sufficient to obtain forgiveness. For some transgressions sacrifice
   was not even effective to obtain forgiveness.
   
   Jews believe that sacrifice is the least important way to gain
   forgiveness from G-d. Repentance is more important. Very few sins
   required sacrifice (per Leviticus). For example., the animal
   sacrifices are only prescribed for unwitting or unintentional sin
   (Leviticus 4:2, 13, 22, 27; 5:5, 15 and Numbers 15:30). The one
   exception is if an individual swore falsely to acquit himself of the
   accusation of having committed theft (Leviticus 5:24-26). Intentional
   sin can only be atoned for through repentance, unaccompanied by a
   blood sacrifice (Psalms 32:5, 51:16-19).
   
   This is re-enforced: "And you shall call upon Me, and go, and pray to
   Me, and I will hearken to you. And you shall seek Me, and find Me,
   when you shall search for Me with all your heart" (Jeremiah 29:13).
   
   Given its relative unimportance even in Biblical days, what comprised
   an acceptable Jewish sacrifice?
   
   Many people think that Jewish sacrifice required blood sacrifice. This
   is not true. The primary commandment about blood is that it shouldn't
   be eaten. (Leviticus 17:10) "And any man from the house of Israel, or
   from the aliens who sojourn among them, who eats any blood, I will set
   My face against that person who eats blood, and will cut him off from
   among his people." This can be paraphrased: "Don't eat blood." The
   next phrase (Leviticus 17:11) goes on to say, "For the soul of the
   flesh is in the blood and I have assigned it for you upon the altar to
   provide atonement for your souls; for it is the blood that atones for
   the soul." This explains why blood is not to be eaten, and that when
   it is used as part of a sacrifice it must be sprinkled on the altar of
   the Temple. Note that it doesn't say, "blood is the only way to atone"
   it says that you shouldn't eat the blood because its only use is for
   sacrifice. Since this is a little confusing lets use an example: we
   can say that all little boys are people, but does that mean that all
   people are little boys?. So Leviticus says "Don't eat blood. You can
   use it for sacrifice," but it doesn't say that blood is the only
   acceptable sacrifice.
   
   What is an acceptable sacrifice? Well, we know what isn't: the Torah
   strictly forbids human sacrifice, unlike most religions of the
   Biblical era.
   
   What kind of sacrifices were allowed? Throughout the Book of
   Leviticus, only distinct species of animals are permitted for use in
   blood sacrifices. There is also atonement by a cereal offering
   (Leviticus 5:11-13), atonement by gold (Num. 31:50), and atonement by
   the burning of incense: "So Moses said to Aaron, 'Take a censer and
   put fire in it from the altar, put incense on it, and take it quickly
   to the congregation and make atonement for them; for wrath has gone
   out from the L-RD." (Numbers 17:11). Remember that prayer and
   repentence must accompany sacrifices.
   
   When Jews were not near the Temple (they lived too far away, or were
   captives as in Babylon) sacrifice was not done by them. King Solomon
   said that even in the days of the Temple prayer could be used by those
   away from the temple to obtain forgiveness (I Kings 8:46-50).
   Synagogues from the time of the Temple have been excavated by
   archeologists. They were used, as they are today, for prayer. Once or
   twice a year sacrifices were sent to the Temple from these Synagogues.
   Now that there is no Temple there are no sacrifices. In accordance
   with the words of Hosea, we render instead of bullocks the offering of
   our lips (Hosea 14:3); i.e., prayer and repentence.