Bigamy law prohibits a person from having more than one spouse at the same time. Most states allow a good faith exception if it was believed a previous spouse was dead or a previous marriage dissolved. No mens rea is required for this offense. Muslims and Mormons have historically practiced polygamy, but the former usually do not do so in the U.S. and authorities are sometimes reluctant to prosecute the latter. Buggery or Bestiality is any type of sexual intercourse with an animal, or, in some states, anal intercourse with a man or women.
Cohabitation requires no proof of sexual intercourse.
It's the least prosecuted public order crime. Incest law prohibits sexual intercourse between a male and a female who are too closely related. The law tends to base relationship on family ties, not genetic ties. All such statutes have been struck down by the Supreme Court. Some states have abolished their sodomy statutes, and in those states where they are still on the books, questions about discrimination against homosexuals remain.