ANSWER: It should first be noted that the word sodomy does not appear not only in the King James Version of the Bible, but also does not occur in the NKJV, NASB, NIV and at least several other translations. According to dictionary.com, this English word did not exist before the 1300's A.D. Webster's Dictionary defines sodomy as having sex (either orally, through the anus, etc.) with a person of the same gender (homosexuality, lesbianism) or with any kind of animal (bestiality). This definition of the term is roughly supported in the Scriptures.
Sodomy, according to a 1913 Catholic Encyclopedia article on lust, is considered a capital sin. Capital sins (according to the church's teachings) are those that, while they are pursued, lead to the committal of other sins. Other than lust, under which sodomy is considered a sub-category, the other capital sins are envy, gluttony, greed, pride, sloth and wrath. Interestingly, in another 1913 Catholic article related to sex, they state that "most theologians" believe that even anal sex within marriage (which they label as a form of sodomy) constitutes adultery and is therefore a sin.
As early as the time of Abraham and Lot (roughly 1900 B.C.), sodomy was considered unacceptable and a sin (Genesis 19:1 - 7). God also reiterated that this practice was against His will when He gave His laws to Israel. Although the Bible usually alludes to this behavior, it without a doubt condemns the practice (Genesis 13:13, 19:5, 19:7, Leviticus 18:22, 20:13 and so on). The city of Sodom, when it existed, was known for its open and shameless indulgence in this wicked behavior, which is why the city lent its name to those who actively pursued such lusts (sodomites).
This sin is an offense against nature that many times was connected with idolatrous practices. This is why the Biblical term 'sodomite' (Strong's Concordance #H6945 as found in Deuteronomy 23:17, 1Kings 14:24, 15:12, 22:46, 2Kings 23:7, etc.), in the Hebrew, means a (male or female) devotee (prostitute) to licentious idolatry. Although allowed and encouraged in some non-Biblical or non-Christian religions, it was NEVER tolerated in the worship of the true God.
The book of Leviticus, which was given directly by the Eternal, contains his instructions for all mankind and not just for Levitical priests or Israelites. It states the following about sodomy between humans and includes what we would call bestiality.
22 No man is to have sexual relations with another man; God hates that . . . 13 If a man has sexual relations with another man, they have done a disgusting thing, and both shall be put to death. They are responsible for their own death . . . 15 If a man has sexual relations with an animal, he and the animal shall be put to death. 16 If a woman tries to have sexual relations with an animal, she and the animal shall be put to death. (Leviticus 18:22, 20:13, 15 - 16)
The New Testament clearly reveals directly to us what happens to those who reject the knowledge of God and His command that this type of behavior is a sin (Romans 1:24, 28). Sodomy, meaning copulation with someone of the same gender, is clearly condemned in the Bible. Sex through the anus within marriage (man and woman), however, is not prohibited in Scripture (though it still may not be wise to do).