Jewish Literacy - Rabbi Joseph Telushkin, p. 263
A famous Yiddish proverb asserts, "It is hard to be a Jew."  One reason, of course, is the ferocious antagonism Jews have often encountered.  Another reason is the demanding nature of Jewish law, 613 Mitzvot in the Torah along and thousands more in the Talmud and legal codes.
Jewish tradition holds that non-Jews are bound by seven laws, presumed to date from the time of that most righteous of gentiles, Noach.  There are six negative laws and one positive one:
  1. Not to deny G-d (for example, idolatry)
  2. Not to blaspheme G-d
  3. Not to murder
  4. Not to engage in incestuous, adulterous, bestial, or homosexual relationships
  5. Not to steal
  6. Not to eat a limb torn from a living animal
  7. To set up courts to ensure obedience to the other six laws (Sanhedrin 56a)
Since each law has extensions and interpretations (see number 4, for example) there are in fact more than seven laws that gentiles are command to observe.
Judaism regards any non-Jew who keeps these laws as a righteous person who is guaranteed a place in the world to come (See Righteous Non-Jews/Chasidei Ummot ha-Olam).  Maimonides believed that a non-Jew was regarded as righteous only if he observed the laws because he believed that G-d ordained them (Mishneh Torah, "Laws of Kings," 8:11); however, this apparently was an innovative view of his, and not a talmudic demand.
The seven Noachide Laws constitute the standard by which Jews assess the morality of a non-Jewish society:  Are there laws against violence and cruelty?  Are there courts to combat anarchy?  The main difference between Noachide and Torah legislation is that the latter commands hundreds of positive actions.  For example, though non-Jews are forbidden to steal, they are not commanded to give charity to the poor, as are Jews (see Tzedakah).
Because Jewish law makes few demands on non-Jews, historically many rabbis have been hesitant to convert non-Jews to the more regorous system of the Torah, believing that it is better that a person be a righteous non-Jew than a nonobservant Jew.  
For further readings:  Aaron Lichtenstein, The Seven Laws of Noach; David Novak, The Image of the Non-Jew in Judaism:  An Historical and Constructive Study of the Noachide Laws.