Murder is another mitzvah that we can easily see applied from the time of Adam. Cain killed Abel, for which he was punished–a clear indication that murder was already prohibited! After the flood, God was very explicit in prohibiting murder, in Genesis 9:5-6. The prohibition against murder includes such additional aspects of life-taking as suicide and abortion. (See Talmud Sanhedrin 57b for the inclusion of abortion among the Noachide laws.)
Like Jews, a non-Jew may kill in self-defense or to save a potential victim from a murderer. This is not, however, license to kill unnecessarily. For example, if someone kills a pursuer when wounding him would have been sufficient to save the victim, he would be liable for murder.