Answer:
   
   In 1981, the late Rabbi Moshe Feinstein addressed this question in
   Igrot Moshe, Choshen Mishpat, Vol. 2 ch. 68. He wrote that the Torah
   prescribes capital punishment for a number of grave offenses,
   including murder, certain types of kidnapping, adultery and idol
   worshiping. The transgressors in these cases, he explained, are
   capable of committing all kinds of atrocities and cruel acts for their
   own benefit. The punishment, however, was not to be inflicted because
   of hatred for the offender or concern for the survival of society, for
   it is the Jewish belief that G-d will punish the offenders (Bava
   Metzia 83b). The purpose of inflicting capital punishment for these
   offenses is to educate people about the severity of the offenses,
   rather than to end the life of the offenders.
   
   Jewish law strongly emphasizes the significance and value of every
   soul, including those of offenders. For this reason only a
   twenty-three member court, a small Sanhedrin, is authorized to try
   capital crimes. Only prominent scholars, well-versed in the wisdom of
   the Torah as well as in other scholarly disciplines, and who possess
   excellent values, qualify for membership on this court. A candidate
   must be humble, G-d fearing, one who despises money, a lover of truth,
   beloved by people for his qualities of goodness and humility, and who
   is sociable, self-composed, compassionate and not the subject of any
   gossip. For this reason a childless person or a very old one, who has
   forgotten the pain of raising children, is not qualified for
   membership on the court, because this person might lack compassion and
   become unduly harsh with offenders. Furthermore, these righteous and
   excellent judges cannot try offenders of capital crimes in a court
   that consists of less than twenty three members. In addition, three
   rows of scholars (candidates for serving on the court) are seated in
   front of the court, watch the proceeding and alert the court to any
   error which might lead to an unlawful conviction. These scholars,
   however, cannot intervene when the error favors the defendant.
   Circumstantial evidence is inadmissible; to convict the defendant two
   qualified witnesses who have no material interest in the case are
   required. Prosecution witnesses are disqualified if they are motivated
   by a desire to testify in order to escape punishment. The witnesses
   must be warned about the graveness of perjury in general and in
   connection with capital punishment in particular. Furthermore, the
   defendant must have been warned prior to committing the crime about
   its severity and must have acknowledged an awareness of it.
   
   Because of all these requirements, execution of criminals in the
   Jewish community was rare, taking place only once in many years.
   Furthermore, capital crimes were tried only at the time of the Holy
   Temple, in which the Great Sanhedrin, consisting of seventy one
   members, was housed. Following the destruction of the Temple, capital
   crimes were not tried in Jewish courts even when they were granted
   jurisdiction by the state to try Jewish criminals according to Jewish
   law.
   
   These rules, however, applied in normal times when murder was rare and
   committed as a result of unrestrained passion or during a dispute over
   property or because of injury to one's honor. In case one killed out
   of cruelty and indifference of the prohibition of murder, or when
   murder became widespread, the strict evidentiary and procedural rules
   in favor of defendants in criminal cases were relaxed, and criminals
   were convicted and executed. Note that the above deals with cases
   where Jews are governing Jews under Jewish law.
   
   With respect to countries such as the United States, one must look at
   the imposition of capital punishment under Noahide law, which applies
   to non-Jewish people, or the power of a king or a state legislature to
   impose capital punishment, based upon the principle of dina
   de'malchuta dina, literally, "the law of the state is the law." The
   authorization for the imposition of capital punishment and the
   relevant evidentiary and procedural rules under Noahide law or the
   principle of dina de'malchuta dina are entirely different from those
   under Jewish law.
   
   The question of capital punishment under the Noahide code was
   discussed in the Talmud. See B. Talmud, Sanhedrin 57a-b. It was
   decided that all seven Noahide laws are capital crimes. (Maimonides,
   Mishneh Torah, Judges, the Laws of Kings 9:14) Under Noahide law one
   may be executed based on the testimony of one witness or a confession,
   and without a prior warning. (Maimonides, ibid, 9:14; Chinuch ch. 26)
   According to one opinion, a criminal might be executed under Noahide
   law based upon circumstantial evidence (Rabbi Z.H. Chayoth, Ma'aritz
   Chayot, Vol. 1 ch. 49). According to Maimonides, non-Jews are required
   to establish a judicial system and apply the Noahide law, including
   the imposition of capital punishment (Maimonides, ibid, 9:14). It
   would appear, then, that American courts might be required under
   Noahide law to impose capital punishment for the violation of any one
   of the seven Noahide laws based upon one-witness testimony,
   circumstantial evidence or a defendant's confession.
   
   Similarly, the imposition of capital punishment by a non-Jewish state
   under the principle of dina de'malchuta dina does not require the
   application of strict evidentiary and procedural rules as in Jewish
   law. For instance, the testimony of one witness or the defendant's
   confession might suffice to convict a defendant (Rabbi B. Ashkenazi's
   commentary (Shita Mekubetzet) on Bava Metzia 83b-84a, citing Ritva)
   Although the principle of dina de'malchuta dina was primarily intended
   to subject Jewish people to the authority of a non-Jewish state, it
   could a fortiori apply also to non-Jewish people. This is because the
   underlying theories of this principle, e.g., the people's implied
   consent to the state's authority, or the power of the state to expel
   disobedient inhabitants, applies to everyone. The restrictions in
   Jewish law on the execution of criminals, delineated by Rabbi
   Feinstein, are limited to trials conducted according to biblical law.
   A Jewish king, however, is not subject to these restrictions and may
   execute criminals more easily than a Jewish court. (Maimonides,
   Mishneh Torah, Kings, 3:10, 4:1-3; Drush ha-Ran, ch. 11). The
   principles which guide a non-Jewish king regarding capital punishment
   are more readily compared to those which guide a Jewish king, rather
   than those which are applied by a Jewish tribunal. Furthermore, some
   scholars believe that the power of a non- Jewish king or government to
   try criminals is based on the Jewish king's prerogatives under Jewish
   law. (Rabbi M. Meterani, Kiryat Sefer, the Laws of Robbery and Lost
   Objects Ch 5; Maimonides, Guide for the Perplexed, Vol. 3, ch. 40).
   Consequently, a non-Jewish king is not subject to the restriction
   applied to Jewish courts with regard to punishment of criminals.
   
   The Reform Movement is against capital punishment. In 1979, the CCAR
   (the Reform rabbinical body) issued the following resolution:
   
     In 1958 and again in 1960, the Central Conference of American
     Rabbis stated its opposition to all forms of capital punishment. We
     reaffirm that position now. Nothing which we have observed during
     the intervening years has shaken our convictions that:
    a. Both in concept and in practice, Jewish tradition found capital
       punishment repugnant, despite Biblical sanctions for it. For the
       past 2.000 years. with the rarest of exceptions, Jewish courts
       have refused to punish criminals by depriving them of their lives.
    b. No evidence has been marshaled to indicate with any persuasiveness
       that capital punishment serves as a deterrent to crime.
    c. We oppose capital punishment under all circumstances.