Typically rendered as “adultery,” this category actually includes far more. Incest, homosexuality, bestiality and other prohibited relationships are all part of this mitzvah. This category also includes the prohibition against castrating any human or animal. (Rape is not part of this category, since the man and woman might be permitted to marry. Rape is, however, prohibited under the category of theft, as the offender takes something from the victim by force.)
This is another mitzvah that we can easily see was given to Adam before it was restated to Noah. Genesis 2:24 addresses the sanctity of marriage, saying that a man should cling to his wife and they should be like a single person. Non-Jews, however, are not obligated in the mitzvah to be fruitful and multiply. The Talmud in Sanhedrin (59b) explains that any commandment that was given twice, namely before Sinai and again at Sinai, applies to both Jews and non-Jews. A mitzvah like being fruitful and multiplying, which was stated before the revelation at Sinai but not repeated, only applies to Jews.
Unlike Jews, non-Jews can marry people forbidden by marriage to a relative after the death of the impeding relative. For example, a man may marry his stepdaughter after the death of his wife, or his daughter-in-law after the death of his son. (It would seem that one may not marry his stepmother even after the death of his father.) Also, Jews would be liable for adultery with a betrothed maiden but non-Jews are not liable for adultery until after the couple’s marriage has been consummated.