Answer:
   
   You had to ask this question? You really had to ask "who is a Jew?"??
   Come on, couldn't you have asked a hard question, like whether Adam
   had a pippik or not? (pippik means navel, a/k/a 'belly button')
   
   For thousands of years the answer was simply someone born of a Jewish
   mother, or someone who undertook a conversion, which involved
   accepting the yoke of the commandments, an immersion in a mikveh
   [ritual bath], and for men, circumcision, the latter two in the
   presense of witnesses. And then came modern times. Hooboy! You sure
   you aren't interested in Adam's pippik?
   
   Anyway, then came modern times, and along came new answers. First the
   oldtimers complained that the newtimers weren't kosher to do a
   conversion and then the newtimers got newfangled about the yoke and/or
   the immersion and/or the circumcision and boy did the oldtimers really
   got unhappy with this and then the issue got more confusing when the
   Israeli government started guaranteeing automatic citizenship to Jews
   resulting in a play it by ear like no one who takes up other religions
   is accepted but the latest round of yelling was when the newtimers
   started accepting Jewish father and Jewish upbringing and at this
   point we give up and are asking all prospective posters of this
   question to first tell us whether Adam had a pippik.
   
   The only thing that is universally agreed is that the practicing of
   other religions is the same as the rejection of Judaism.
   
   Even within Orthodoxy the answer gets, uh, "flexible" at times. (You
   thought this was just newfangled vs oldfangled? Heh!) When the Nazis
   were trying to figure out whether to murder the Karaites quickly or
   slowly, they asked several Orthodox rabbis if the Karaites were Jewish
   or not. (You figured out the answer? Maybe you belong in yeshiva!)
   Nineteenth century Samaritan massacres by Islamic zealots were stopped
   when they got official word that Samaritans are Jews, i.e., people of
   the book. There have been conflicting answers regarding the Ethiopian
   Jews.
   
   Another bit of Orthodox "flexibility" comes regarding Conservative
   conversions. Such a person (a sofek) is not counted as Jewish for
   anything positive, but is often treated as Jewish for things negative,
   just in case. Thus, a sofek may not be called to the Torah, or even be
   counted for a minyan, but would not be treated as a Shabbos goy. (He
   would be expected to do a divorce in the traditional manner, but this
   shouldn't be a problem, since as a Conservative he holds by that too.)
   Conservatives often act the same towards Reform conversions, and even
   within all three movements, there is often rejection of lenient
   leaning conversions.
   
   Reform Judaism rules that the children of two Jewish parents are
   considered Jewish. Reform also rules that when one parent is Jewish
   and the other gentile, the identity of the child as Jewish must be
   established subsequently through Jewish education and positive Jewish
   acts such as Bar Mitzvah, Confirmation, etc. This is known as the
   "[5]Patrilineal descent" ruling, because it considers the child of a
   Jewish father and gentile mother to be Jewish without a conversion
   ceremony, as opposed to "Matrilineal descent" in which the child of a
   Jewish woman is automatically Jewish, irrespective of paternity or
   subsequent practice. If you want to look at [6]the text of the
   decision, which is a recurring debate topic on S.C.J, it may be found
   at the URL
   [7]http://www.ccarnet.org/cgi-bin/resodisp.pl?file=mm&year=1983.
   
   While countless treatises have been written on this subject, some
   readers recommend the Chabad/Lubavitch booklet "Who is a Jew?" by R'
   J. Immanuel Schochet, available from SIE, 788 Eastern Pkwy, Brooklyn,
   NY 11213.