Why do Jews no longer sacrifice animals?
Generally speaking, the vast majority of Jews do not engage in animal sacrifice primarily because they no longer have a Temple in which to do so. However, there are a very few ultra-Orthodox Jews who have limited forms of animal sacrifice. For example, there is a controversial folk custom that a few ultra-Orthodox will do for Yom Kippur called kaparot:
The rooster or hen is whirled above the individual’s head three times while the following words are recited: “This is my substitute, my vicarious offering, my atonement. The cock or hen shall meet death, but I shall enjoy a long, pleasant life of peace” (Koltach, Alfred; pg. 239). After these words are said the chicken is slaughtered and either eaten by the person who performed the ritual or given to the poor.
Because kaparot is a controversial custom, in modern times, Jews who practice kaparot will often substitute money wrapped in white cloth for the chicken. The same biblical verses are recited, and then the money is swung about the head three times as with the chicken. At the conclusion of the ceremony the money is given to charity.