We see reference to cremation in the Old Testament book of Amos.¹  Among the early Jews however, burial was the normal practice.  This was due to their belief that cremation of the dead was a desecration of a work of God.

In early Christianity, in light of the resurrection, cremation of the body after death was not practiced due to the belief that the body would not be resurrected if it were destroyed.  In today's society, however, mostly due to economic considerations, cremation is practiced.  There are groups within Christianity that still forbid its members from cremating their dead, however.

My own opinion is that there is nothing wrong with cremation as long as it is not done out of disrespect for the body, or out of disrespect for the resurrection of the dead.

Bible References:

¹ (Amos 6:10)