It occurred to me (belatedly), after the opening of the movie “Noah,” that I should post the 7 laws of the “B’nei Noach” — the Children of Noah — the rabbinic term for all people other than the B’nei Yisrael — the Children of Israel.
First, it should be pointed out, these laws are not found as such in the text of Torah itself, although they’re derived from there. The laws, found in some commentaries and chumashim (e.g. Hertz), ultimately have their basis in Sanhedrin 56a (Talmud). The list is as follows, but does not always appear in the same order:
1. The prohibition of idolatry: Don’t worship idols.
2. The prohibition of murder: Don’t murder.
3. The prohibition of theft: Don’t steal.
4. The prohibition of sexual immorality: Don’t commit adultery.
5. The prohibition of blasphemy: Don’t bring disrespect on G-d’s Name.
6. The prohibition cruelty to animals: Don’t eat the flesh of a live animal.
7. Maintain a just system of laws and courts: Provide legal recourse
Two online articles with fuller discussions:
To some extent, these laws — especially the 7th — also fit in with Rabbi Shimon b. Gamliel’s statement: “On three things the world endures: Justice, Truth and Peace.”  This is particularly appropriate as we now begin the learning of Pirkei Avot.
We can see in these laws, as specified by the rabbis, that all people are required to create a just, stable society.
The rabbis would have had some problems with certain Christian societies that used statues in worship, and Buddhist societies who worshiped statues of Buddha (or others), even if those societies otherwise conformed closely to the ideal presented. They would however have been in close sympathy with the absolute prohibition of idols in Islam.
The Protestant Reformation, iconoclastic in nature, had much to do with strictly implementing the first law, too. It was also in the spirit of this law that the Taliban destroyed two large statues of Buddha in Afghanistan a few years ago, despite the aesthetic loss deplored by the world.
It’s likely that readers of this post, and other articles about this topic, will have diverse feelings about the need to abolish idols. That in itself demonstrates its continuing relevance.
As for the prohibition against “blasphemy,” I take it in a simple sense: Don’t believe that we can avoid the consequences of our actions and don’t encourage other people to believe that they can, either.
Regarding not being cruel to animals:
In the Eagles’ song “Hotel California,” the ultimate image of the depravity of the singer’s environment is the feast “in the master’s chambers” — “…They stab it with their steely knives but they just can’t kill the beast…”  Meant to horrify us, it’s a grotesque image of people who no longer care at all about the suffering and pain they cause in the pursuit of their own pleasures. By their mutual agreement, they create a culture in which this is not only tolerated, but expected; even relished.
The rabbis were similarly disgusted and horrified at the depths of cruelty to which human beings could sink, and urged us all to maintain at least minimum standards of compassion.
A culture or society that tolerates heartless cruelty to persons, animals or the environment, cannot survive without changing, as Shimon ha-Tzadik used to say:
“On three things the world stands. On Torah, on worship, and on acts of kindness.” 
It was true 2,000 years ago.
It’s still true today.
 Pirkei Avot 1:18
 Don Felder, Glenn Frey and Don Henley; “Hotel California“; the song was released in 1977, but I haven’t yet found the actual copyright date.
 Pirkei Avot 1:2