Burial is a positive commandment.  Deuteronomy (21:23)  his body shall not remain overnight on the tree, but you shall surely bury him that day, so that you do not defile the land which the Lord your God is giving you as an inheritance; for he who is hanged is accursed of God.

Ashes to ashes, dust to dust. (Gen. 3:19)  In the sweat of your face you shall eat bread
Till you return to the ground, For out of it you were taken; For dust you are,And to dust you shall return.

Cremation was not unknown to the early Hebrews, and “burning” was one of the four death penalties imposed by the biblical code for a number of offenses (Lev. 20:14; 21:9)

Leviticus 20:14

14 If a man marries a woman and her mother, it is wickedness. They shall be burned with fire, both he and they, that there may be no wickedness among you.

Leviticus 21:9
9 The daughter of any priest, if she profanes herself by playing the harlot, she profanes her father. She shall be burned with fire.

Reserved for criminals — Josh. 7:15, 25; Isa. 30:33

In Judaism, burning of the human body is considered a disgrace. Regarding the execution of the wicked Achan and his sons and daughters the verse states: “And all Israel stoned him with stones, and burned them in the fire. So God rescinded His anger” (Joshua 7:25). Similarly, the righteous King executed the priests of idol worship:  He executed all the priests of the high places who were there, on the altars, and burned men’s bones on them; and he returned to Jerusalem (2 Kings 23:20).

Edomite King (Amos 2:1)  For three transgressions of Moab, and for four, I will not turn away its punishment,  Because he burned the bones of the king of Edom to lime.

King Saul and his sons were burned but the fire was not too hot and did not consume the bones.  The bones were buried under a tree.  Even so, the nation suffered three years of famine for burning those bodies (2 Samuel 21:1).  1 Samuel (31:11–12)  11 Now when the inhabitants of Jabesh Gilead heard what the Philistines had done to Saul, 12 all the valiant men arose and traveled all night, and took the body of Saul and the bodies of his sons from the wall of Beth Shan; and they came to Jabesh and burned them there.

For more from a Christian perspective, visit http://www.ecclesia.org/truth/cremate.html

This note from Rabbi Ullmann concerning the Jewish traditions and beliefs about cremation:

“One who is intentionally cremated not only uproots a positive Torah requirement to bury, and transgresses a negative Torah prohibition of leaving a body unburied, but also transgresses a prohibition against cremation. In addition, just as the soul suffers great agony when its departure from the body is unnecessarily prolonged (as when the body is put in a Mausoleum), so too the soul suffers tremendously from the extremely abrupt process of cremation.

Furthermore, one who has his body cremated will not merit resurrection: I believe with complete faith that there will be a resurrection of the dead, when the wish emanates from the Creator. One explanation is that cremation destroys even the extremely hard luz bone from which a buried body is reconstituted. This may be understood by an analogy: while a planted seed fully rots and even provides nutrient for the sprout, a burnt seed doesn’t even sprout. In truth, cremation is less a physical impediment to resurrection than a spiritual one. G-d can do anything He chooses, and in fact all Jews who were burned against their will throughout history will certainly merit resurrection. Rather, one who willfully has his body cremated asserts his disbelief in the future reunification of body and soul. Regarding this our Sages warn, One who rejects the idea of resurrection will have no part in it.”