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http://www.chabad.org/library/article_cdo/aid/510874/jewish/Why-does-Jewish-law-forbid-cremation.htm

The Biblical Commandment

Man’s soul comes from Above, “He breathed into his nostrils the soul of life,”and when its earthly mission has been accomplished it rises back to G-d, returning to its source.

The body, on the other hand, was taken from the ground — “the L-rd G-d formed man of dust from the ground”— and must therefore return to the earth. This is expressed in the words that G-d tells Adam, the first man, “For dust you are, and to dust you will return.”

This concept is reiterated in Deuteronomy,where we are commanded to bury the dead: “You shall bury him on that day.” The Jerusalem Talmud explains that this requires us to bury the body in its entirety, not after it has been diminished through cremation or in any other manner: “You must bury him in entirety, not partially. From this verse we extrapolate that the command was not fulfilled if the person was partially buried.”

Cremating a body destroys most of the body, making burial of the flesh impossible, and thus violates the biblical command.

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Our Responsibilities Vis-à-Vis the Human Body

In Jewish law, the human body belongs to its Creator. It is merely on loan to the person, who is the guardian of the body, but he or she has no right to deface it in any way. The body must be “returned” in its entirety, just as it was given.

Additionally, Man was created in “G-d’s image and likeness.”Any violation of the human body is considered, therefore, to be a violation of G-d Himself.

This general principle and law governs many of our laws, like those prohibiting self-mutilation or tattoos, and requiring us to do our utmost to keep ourselves from danger by maintaining proper hygiene and the like. This principle applies after death, too; any mutilation of the dead is prohibited.