There are big differences of opinion amongst different religions about embalming.  Here is a  brief look at some of the larger faiths positions.

All of the major branches of the Christian faith, including Catholic rites, allow embalming, with the exception of Eastern Orthodoxy, which only allows embalming if required by law or other necessity.  

The Book of Mormon and The Church of Jesus Christ of Latter-day Saints are not against embalming. Often, due to the custom of church members dressing the deceased, embalming is given preference.

Buddhism and Taoism beliefs accept embalming as a valid practice.

Many authorities hold Hinduism does not accept embalming. In practice, this is not an adamant prohibition and embalmings for those of Hindu faith are known to happen, generally for repatriation to India or the South Pacific and for the purposes of viewing and funerary rites at the family home.

Muslims are required to be buried within 24 hours of death if possible. Although embalming is forbidden. The body is still washed and prepared specifically for interment. This procedure is to be done according to the last will of the deceased, usually by a close relative of the deceased who is of the same gender. He or she is then dressed in a plain white burial shroud.  

Traditional Jewish law generally forbids embalming, and burial is to be done as soon as possible - preferably within 24 hours. However, under certain circumstances, embalming may be permitted if it is impossible to bury a person immediately