These seven commandments were given to all mankind after the flood (hence they are known as the Noach-ide Laws) and anyone desiring a harmonious, G-d fearing life on earth as well as a place in the World to Come must follow them. Jews believe that it does not matter what religion you belong to, but rather how you act that is important. There's no need for a messiah for salvation (other than G-d Itself). These last two concepts in are conflict with the teachings of christianity and some other religions, but have their basis in the written word of G-d (the Torah):
1) Idolatry (in whatever form) is forbidden.
2) Blasphemy and swearing falslely by G-d's name is forbidden.
3) Murder is forbidden.
4) Prohibited sexual relations (incest, animals, same sex) are forbidden.
5) Theft is forbidden.
6) Eating a limb from a living animal is forbidden.
7) Mankind must establish courts of justice.
Righteous Gentiles are sometimes also called "Ethical Monotheists"
The Laws of Noah, The Universal Laws of Mankind, or what ever title you chose to know them by, are a set of Laws (Commandments) that are found in the Holy Scriptures. Specifically, Genesis chapters 1 through 11. Abraham, the Patriarch, is chosen to be the father on many nations (Jewish) in the subsequent chaper. The remaining chapters of Genesis (12 through 50), and the remaining books of the Torah, are given to and binding upon the House of Israel. There, too, we find the emphasis of the Bible to change from the relationship of G-d and the person to the relationship between G-d and His chosen people.
These Universal Laws give the Gentile Nations (70) Hope and Meaning in our lives. Let's face it, not everyone can be, nor desires to be Jewish. Almost everyone, however, does want to find meaning in this world and a share in the World to Come. These laws do just that for us. It is through strict observation of these Laws that the Gentile (non-Jew) becomes righteous and brings him or herself closer to The Almighty!
You may notice that these Laws are not unlike the 10 Commandments G-d later gave the Israelites. There were 10 generations between Adam and Noah and then 10 more generations between Noah and Abraham (the Jews were given 10 Commandments). The Noachides (righteous gentiles) pre-dated the Hebrew Nation by over 400 years! Some authors claim that the Rainbow (which has 7 colors...1 for each of the seven Noachide Laws) had never been seen before this moment in history since it was made on the sixth day of Creation!
Idolatry, Sexual Immorality and Murder are the 3 "Cardinal Sins". These must not be transgressed even when threatened with death. The others may be performed to save your life.
To learn more about the Noachide Laws see